The terms "retro" and "arcade" are very broad; they can range from a single-screen game like in 1980s to a Danmaku from the 2000s.
Platform?, Beat 'em up?, shoot' em up?, run and gun? fighting?
Without much more detail, I could recommend the games of "locomalito." He's an independent developer who usually makes arcade-style games. The bad thing is that you won't find him on Itch, but here's the link to his page. His games are usually free, but he has a couple of paid ones on Steam.
You also don't clarify if your machine uses a CRT and if you're limited to a certain resolution.
I have a '90s-inspired arcade shoot em up. It's designed for an vertical 800x600 monitor, but it runs on any modern computer. It's paid, but if you contact me privately, I can send you an Itch key if you're interested.