The best arcade games like Dynamite Cop are Die Hard Arcade, Streets of Rage 4 and Fight'N Rage. Below are 7, each with the reason it is here — and, at the end, what filtering to arcade costs you.
Filtering to arcade means you want short runs and a score, not a campaign. It is the right filter when what you liked was the one-more-go feeling.
What you get: A complete experience in twenty minutes, and a skill you keep. Arcade design is measured in the moment after you lose.
What made Dynamite Cop worth playing in the first place is covered on the full list. This page is the arcade part of that answer, and only the arcade part.
The direct predecessor, and the same weapon-grabbing chaos.
The best modern beat-em-up, and it honours the arcade originals.
An indie brawler with branching routes and real depth.
The most fun four-player brawler in years.
Same arcade brevity, fantasy instead of skyscrapers.
Dreamcast contemporary where the stage is also the weapon.
Saturn brawler with branching paths and a huge cast.
Story and progression. Arcade games repeat on purpose, and if you want to be pulled somewhere they will not do it.
Specifically, these are strong answers for Dynamite Cop that are not arcade games, so they are not on this page:
The full list is on games like Dynamite Cop — 9 picks, no genre filter.
Die Hard Arcade. The direct predecessor, and the same weapon-grabbing chaos.
No. Dynamite Cop released on the Sega Dreamcast, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
They were designed to end. A machine that let you play for an hour on one coin did not earn its floor space, so difficulty was the business model.
Constantly, mostly by small teams. Several of the best beat-em-ups and run-and-guns of the last decade are new games built on forty-year-old design rules.
By hand. Each pick was written for the full Dynamite Cop list first, on what the game actually does, and this page is the part of that list that is arcade — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the arcade guide for where to start in the genre generally.