All you need is a Halo patch, it has nothing to do with compatibility. I will leave below the link to the BUNGIE website where you need to get the patch in order to update the game, so it can run in Windows 10.
https://www.bungie.net/en/Forum/Post/
https://www.bungie.net/en/Forums/Post/64943622?page=0&sort=0&showBanned=0&path=0
Once you are there click on Halo PC 1.0.10 and that would do it.