My experience while dual-booting both Windows 7 and Windows 10 is that more games run on Windows 7, and games run better on Windows 7.
1. Windows 10 has DirectX 12, but Windows 7 has Vulkan, which does the same thing as DirectX 12. And Vulkan seems to be the favourite between the two by current developers, due to its cross-platform abilities and open-source nature. The only games that you'll miss out on by not having Windows 10 and DirectX12 are Microsoft exclusive games (as Microsoft wants to force people to Windows 10 by withholding their games from other markets).
And there ends the only semi / potential benefit of gaming on Windows 10 that I'm aware of.
2. If you play old games, then Windows 7 natively had better compatibility for them. Some games I haven't even been able to get to run in Windows 10. I can't immediately think of the list off the top of my head, but the MechWarrior 4 series is one of the recent ones, and there have been others, too. Granted, MechWarrior 4 Mercenaries still takes some tweaking in Windows 7 to get it running, but at least I was able to get it running.
3. Another point is that, though many older games can be played in Windows 7 and 10 with some tweaking, they might take more tweaking to get working in Windows 10 than in Windows 7. There are some compatibility features that are just present in Windows 7 which are either turned off by default in Windows 10, or are missing and need to be added manually. This can included absent system DLL files, or something like .NET Framework 3.5 for legacy game support which needs to be manually enabled in Windows 10.
4. While some people mention that FPS between Windows 7 and Windows 10 should be mostly similar (some more in one OS, and some more in the other), there are some definite and even serious caveats to that:
- Due to Windows 10's ironically-titled * Game Mode which is turned on by default, Windows 10 seems to lose some FPS in a lot of situations unless that Game Mode is disabled.
- If you play Ubisoft games, they get a chunk more FPS in Windows 7 than they do in Windows 10. Sure, Ubisoft is just bad at PC coding, or whatever else you want to explain it as, but the fact is, Ubisoft games get a chunk more FPS in Windows 7 than they do in Windows 10.
5. Also, Windows 10 interrupts gaming sessions with background downloading, updates, system resets, and the general diminished stability that Windows 10 has compared to Windows 7.
6. Lastly, there are mounds more community guides, fixes, and tweaks designed for older games running in Windows 7 than there are for older games running in Windows 10.
In my view, without a doubt, Windows 7 is more stable, more reliable, and more compatible with a wider range of games than Windows 10 is. And Windows 7 is at least on-par with Windows 10 in the area of FPS. If you just want a rock-solid gaming rig that can do just about everything while not interrupting or obstructing your experiences, then I think that Windows 7 is the way to go, as I think that Windows 10 is a compromised experience both in and out of games.
Update: The below video is not representative of newer (maybe 1803 onwards?) versions of Windows 10, which generally show parity in performance between having Game Mode on or off.
* LTT made a video comparing Windows 10 running games in Game Mode to running games with Game Mode turned off: