OK, you asked for IT, Johan:
DXError.log
--------------------
[07/16/15 09:17:08] module: DXWSetup(Mar 30 2011), file: dxwsetup.cpp, line: 229, function: CDXWSetup::InitInstallEngine
Sections are not initialized.
--------------------
[07/16/15 09:17:08] module: DXWSetup(Mar 30 2011), file: psheets.cpp, line: 705, function: PreinstDlgProc
CDXWSetup::InitInstallEngine() failed.
--------------------
[07/16/15 09:21:21] module: DXWSetup(Mar 30 2011), file: dxwsetup.cpp, line: 229, function: CDXWSetup::InitInstallEngine
Sections are not initialized.
--------------------
[07/16/15 09:21:21] module: DXWSetup(Mar 30 2011), file: psheets.cpp, line: 705, function: PreinstDlgProc
CDXWSetup::InitInstallEngine() failed.
--------------------
[07/16/15 09:22:05] module: DXWSetup(Mar 30 2011), file: dxwsetup.cpp, line: 229, function: CDXWSetup::InitInstallEngine
Sections are not initialized.
--------------------
[07/16/15 09:22:05] module: DXWSetup(Mar 30 2011), file: psheets.cpp, line: 705, function: PreinstDlgProc
CDXWSetup::InitInstallEngine() failed.
DirectX.log
07/16/15 09:17:04: DXWSetup: ***** DXWSETUP *****
07/16/15 09:17:04: DXWSetup: WinMain()
07/16/15 09:17:04: DXWSetup: Bing Bar is already installed, skipping offer
07/16/15 09:17:04: DXWSetup: IsIA64(): not IA64.
07/16/15 09:17:04: DXWSetup: Unable to get Version on target file C:\WINDOWS\system32\directx\websetup\dsetup.dll
07/16/15 09:17:04: DXWSetup: Installed file C:\WINDOWS\system32\directx\websetup\dsetup.dll
07/16/15 09:17:04: DXWSetup: Unable to get Version on target file C:\WINDOWS\system32\directx\websetup\dsetup32.dll
07/16/15 09:17:04: DXWSetup: Installed file C:\WINDOWS\system32\directx\websetup\dsetup32.dll
07/16/15 09:17:04: DXWSetup: GetDXVersion(): Unable to get RC string from registry.
07/16/15 09:17:04: DXWSetup: DirectX Version: 4.09.00.0904.00
07/16/15 09:17:04: DXWSetup: Setup Version: 4.09.00.0904.00
07/16/15 09:17:04: DXWSetup: A newer version of DirectX have been installed already.
07/16/15 09:17:08: DXWSetup: CDXWSetup::CDXWSetup()
07/16/15 09:17:08: DXWSetup: CDXWSetup:

ownloadDXUpdate()
07/16/15 09:17:08: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x1, SubStatus = 0x0
07/16/15 09:17:08: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x3, SubStatus = 0x0
07/16/15 09:17:08: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x2, SubStatus = 0x0
07/16/15 09:17:08: DXWSetup: OnStartInstall(): DLSize = 81, InstallSize = 0
07/16/15 09:17:08: DXWSetup: OnStartComponent(): ID = DXUpdate, DLSize = 81, InstallSize = 0, str = %DirectX_Setup%
07/16/15 09:17:08: DXWSetup: OnComponentProgress(): Phase = 0, Progress = 0
07/16/15 09:17:08: DXWSetup: OnStopComponent(): ID = DXUpdate, hr = 0x0, Phase = 9, str = %DirectX_Setup%, status = 0x0
07/16/15 09:17:08: DXWSetup: OnStopInstall(): hr = 0x0, str = (null), status = 0x0
07/16/15 09:17:08: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x3, SubStatus = 0x0
07/16/15 09:17:08: DXWSetup: WM_APP_DOWNLOADDXUPDATE
07/16/15 09:17:08: DXWSetup: CDXWSetup::InitInstallEngine()
07/16/15 09:17:08: DXWSetup: CDXWSetup::InitInstallEngine(): Sections are not initialized.
07/16/15 09:17:08: DXWSetup: PreinstDlgProc(): CDXWSetup::InitInstallEngine() failed.
07/16/15 09:17:08: DXWSetup: WM_APP_ENDDOWNLOAD
07/16/15 09:17:14: DXWSetup: CDXWSetup::~CDXWSetup()
07/16/15 09:17:16: DXWSetup: CreatePropertySheet() returns -9.
07/16/15 09:17:16: DXWSetup: Deleted file C:\WINDOWS\system32\directx\websetup\dsetup.dll.
07/16/15 09:17:16: DXWSetup: Deleted file C:\WINDOWS\system32\directx\websetup\dsetup32.dll.
07/16/15 09:21:13: DXWSetup: ***** DXWSETUP *****
07/16/15 09:21:13: DXWSetup: WinMain()
07/16/15 09:21:13: DXWSetup: Bing Bar is already installed, skipping offer
07/16/15 09:21:13: DXWSetup: IsIA64(): not IA64.
07/16/15 09:21:13: DXWSetup: Unable to get Version on target file C:\WINDOWS\system32\directx\websetup\dsetup.dll
07/16/15 09:21:13: DXWSetup: Installed file C:\WINDOWS\system32\directx\websetup\dsetup.dll
07/16/15 09:21:13: DXWSetup: Unable to get Version on target file C:\WINDOWS\system32\directx\websetup\dsetup32.dll
07/16/15 09:21:13: DXWSetup: Installed file C:\WINDOWS\system32\directx\websetup\dsetup32.dll
07/16/15 09:21:13: DXWSetup: GetDXVersion(): Unable to get RC string from registry.
07/16/15 09:21:13: DXWSetup: DirectX Version: 4.09.00.0904.00
07/16/15 09:21:13: DXWSetup: Setup Version: 4.09.00.0904.00
07/16/15 09:21:13: DXWSetup: A newer version of DirectX have been installed already.
07/16/15 09:21:21: DXWSetup: CDXWSetup::CDXWSetup()
07/16/15 09:21:21: DXWSetup: CDXWSetup:

ownloadDXUpdate()
07/16/15 09:21:21: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x1, SubStatus = 0x0
07/16/15 09:21:21: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x3, SubStatus = 0x0
07/16/15 09:21:21: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x2, SubStatus = 0x0
07/16/15 09:21:21: DXWSetup: OnStartInstall(): DLSize = 81, InstallSize = 0
07/16/15 09:21:21: DXWSetup: OnStartComponent(): ID = DXUpdate, DLSize = 81, InstallSize = 0, str = %DirectX_Setup%
07/16/15 09:21:21: DXWSetup: OnComponentProgress(): Phase = 0, Progress = 0
07/16/15 09:21:21: DXWSetup: OnStopComponent(): ID = DXUpdate, hr = 0x0, Phase = 9, str = %DirectX_Setup%, status = 0x0
07/16/15 09:21:21: DXWSetup: OnStopInstall(): hr = 0x0, str = (null), status = 0x0
07/16/15 09:21:21: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x3, SubStatus = 0x0
07/16/15 09:21:21: DXWSetup: WM_APP_DOWNLOADDXUPDATE
07/16/15 09:21:21: DXWSetup: CDXWSetup::InitInstallEngine()
07/16/15 09:21:21: DXWSetup: CDXWSetup::InitInstallEngine(): Sections are not initialized.
07/16/15 09:21:21: DXWSetup: PreinstDlgProc(): CDXWSetup::InitInstallEngine() failed.
07/16/15 09:21:21: DXWSetup: WM_APP_ENDDOWNLOAD
07/16/15 09:21:29: DXWSetup: CDXWSetup::~CDXWSetup()
07/16/15 09:21:31: DXWSetup: CreatePropertySheet() returns -9.
07/16/15 09:21:31: DXWSetup: Deleted file C:\WINDOWS\system32\directx\websetup\dsetup.dll.
07/16/15 09:21:31: DXWSetup: Deleted file C:\WINDOWS\system32\directx\websetup\dsetup32.dll.
07/16/15 09:22:02: DXWSetup: ***** DXWSETUP *****
07/16/15 09:22:02: DXWSetup: WinMain()
07/16/15 09:22:02: DXWSetup: Bing Bar is already installed, skipping offer
07/16/15 09:22:02: DXWSetup: IsIA64(): not IA64.
07/16/15 09:22:02: DXWSetup: Unable to get Version on target file C:\WINDOWS\system32\directx\websetup\dsetup.dll
07/16/15 09:22:02: DXWSetup: Installed file C:\WINDOWS\system32\directx\websetup\dsetup.dll
07/16/15 09:22:03: DXWSetup: Unable to get Version on target file C:\WINDOWS\system32\directx\websetup\dsetup32.dll
07/16/15 09:22:03: DXWSetup: Installed file C:\WINDOWS\system32\directx\websetup\dsetup32.dll
07/16/15 09:22:03: DXWSetup: GetDXVersion(): Unable to get RC string from registry.
07/16/15 09:22:03: DXWSetup: DirectX Version: 4.09.00.0904.00
07/16/15 09:22:03: DXWSetup: Setup Version: 4.09.00.0904.00
07/16/15 09:22:03: DXWSetup: A newer version of DirectX have been installed already.
07/16/15 09:22:05: DXWSetup: CDXWSetup::CDXWSetup()
07/16/15 09:22:05: DXWSetup: CDXWSetup:

ownloadDXUpdate()
07/16/15 09:22:05: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x1, SubStatus = 0x0
07/16/15 09:22:05: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x3, SubStatus = 0x0
07/16/15 09:22:05: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x2, SubStatus = 0x0
07/16/15 09:22:05: DXWSetup: OnStartInstall(): DLSize = 81, InstallSize = 0
07/16/15 09:22:05: DXWSetup: OnStartComponent(): ID = DXUpdate, DLSize = 81, InstallSize = 0, str = %DirectX_Setup%
07/16/15 09:22:05: DXWSetup: OnComponentProgress(): Phase = 0, Progress = 0
07/16/15 09:22:05: DXWSetup: OnStopComponent(): ID = DXUpdate, hr = 0x0, Phase = 9, str = %DirectX_Setup%, status = 0x0
07/16/15 09:22:05: DXWSetup: OnStopInstall(): hr = 0x0, str = (null), status = 0x0
07/16/15 09:22:05: DXWSetup: OnEngineStatusChange(): EngineStatus = 0x3, SubStatus = 0x0
07/16/15 09:22:05: DXWSetup: WM_APP_DOWNLOADDXUPDATE
07/16/15 09:22:05: DXWSetup: CDXWSetup::InitInstallEngine()
07/16/15 09:22:05: DXWSetup: CDXWSetup::InitInstallEngine(): Sections are not initialized.
07/16/15 09:22:06: DXWSetup: PreinstDlgProc(): CDXWSetup::InitInstallEngine() failed.
07/16/15 09:22:06: DXWSetup: WM_APP_ENDDOWNLOAD
------------------------------------------------------------------------
So, I cannot install DirectX 9 on Windows 10.