Have you tried Double Action Boogaloo? It is probably right up your alley if you like Fistful of Frags.
You might enjoy Quake or other arena shooters like Warsow or Ratz Instagib.
If you want to try something new that still fits the bill I’d go with Enter the Gungeon or Dead Cells. Both are easy to pick up but incredibly challenging to master. Both are roguelikes with a short time per run, so the game already does the job of breaking itself into short play periods. And both are action heavy.