C64's competition were the Atari 400, 800, XL and XE lines. Most games came out for both platforms. Atari's player missle system was both an advantage and a disadvantage in some respects.
The ST and Amiga were competitors but completely different platforms than their respective predecessors.
When you're talking Mac - the Apple II would have been the contemporary of the C64 and Atari 8-bit lines. There were games on Apple computers as well, but I suspect not as many. They were completely dysfunctional and the Apple IIgs was a really fun machine.
Hell of a game.
They built a machine to compete with the C64 at the time when Amiga was the new thing.
They were popular in Europe, where they were cheap. In fact, in the UK, the 512K Atari ST with mono screen and mouse was slightly cheaper upgrading a 128K Mac to 512K (£750 vs £800).
The Atari ST was slightly faster than the Mac, had a better monochrome screen, and could run all Mac software, albeit not legally. (You either bought a plug-n cartridge that took Mac ROMs or used MacBongo, a ripped-off version loaded from disk.)
Atari practically owned the gaming business with its home games consoles, and its first home computers -- the Atari 400 and 800, launched in 1979 -- were the best games machines around at the time.
The Atari ST was the one the audio folks used, and it did play games, just not as well as the Amiga.
Curiously enough, the Amiga was developed by staff from Atari, while the Atari ST was developed by staff from Commodore. (This was after Jack Tramiel left Commodore and bought Atari, which he ran with his sons.)
Ataris were never really that good for gaming either, but they were used a lot by pro audio folks. They had superior midi capabilities and programs.