The best arcade games like Tekken 3 are Tekken 8, Virtua Fighter 5: Ultimate Showdown and Soulcalibur VI. Below are 8, 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 Tekken 3 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 current entry, and the single-player content is generous again.
The purest 3D fighter, and the most technically respected.
3D fighting with weapons, and a proper story mode.
Faster 3D fighting built around counters.
If you want the best current fighting game with the most to do offline.
Same era, arena fighting instead of one-on-one.
The best single-player campaign in any fighting game.
Capcom's 3D fighter with a full story mode, still a favourite.
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 Tekken 3 that are not arcade games, so they are not on this page:
The full list is on games like Tekken 3 — 9 picks, no genre filter.
Tekken 8. The current entry, and the single-player content is generous again.
No. Tekken 3 released on the PlayStation, 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 Tekken 3 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.