It runs fine on Windows 8.1
Where is the game installed. The game should not be installed in the programs folder.
You might also need a 3rd party codecs since Windows 8.1 is likely missing some audio and video codecs install Sharky's or K-lite codecs.
Also please run dxdiag.exe and post in spoiler tags.
I don't agree. Literally every time I have attempted to install outside of the default STEAM location (C:\Program Files (x86)\Steam\steamapps\common\Fallout New Vegas), the game fails to start propely. Put it back to C:\Program Files (x86)\Steam\steamapps\common\Fallout New Vegas and it works perfectly.
On my end Steam is not installed in programs folder but in C:\Games\Steam\etc\etc\etc\. I never had any issues there. I actually do not install anything in the programs folder.
My alternate (and most used) STEAM location is the one that doesn't work for me, C:\Steam Games\steamapps\common