SpeedBo: The Mechwarrior series is one of the best. Highly recommended.
As for Mech 3 on windows 10. I've tried it... It seems to run fine, until a mech you're fighting randomly bounces off into the sky. It's like they get hit, or take a step and it just goes straight up out of sight.
It makes it very hard to play the game.
Hmmm, did you limit framerates to maybe 30fps or 60fps? Sounds like some physics, graphics, and/or DirectX stuff is going out of whack here.
Also, b/c this is an older game (that used DirectX 6.1) - yeah, that could be another problem. So, you might want to install and/or inject DGVoodoo or any DirectX wrappers that support older DX versions, just to try to interrupt/intercept the DX10 calls to get them to run properly w/ wrappers that act more like older DX versions.
EDIT:
You also, might want to check the PC Gaming Wiki too:
https://www.pcgamingwiki.com/wiki/MechWarrior_3