Yes, Red Ace Squadron runs on 64-bit systems. I've just tested it on a 64-bit Windows 10 PC and it worked fine, so it will most likely run on older Windows versions as well, all the way back to Windows 95.
Based on this, I'm guessing that the other games from this developer will also work on 64-bit systems. However, in case you run into compatibility trouble with any of them, all you have to do is to install the DOSBox emulator and run the game through it.
Tip: After DOSBox has been installed, type intro mount to learn how to mount game directories inside the app so you can call them through the command prompt (the way DOSBox launches apps and games)