Because Cactus McCoy is a Flash-based game, you cannot simply "install" it like a standard modern AAA title. Instead, you need the original game file (SWF) and a way to run it on Windows 10 or 11.
For the most stable experience, use BlueMaxima's Flashpoint, a massive preservation project. By downloading the Flashpoint launcher, you can search for "Cactus McCoy" and play it offline with full save support. System Requirements for Windows
Even though it was originally a browser game, running it locally requires a few minimum specs to ensure the "Enemigo Juggling" and fast-paced brawling stay smooth: