The best arcade games like Star Fox 64 are Sin and Punishment: Star Successor, Panzer Dragoon Orta and Rez Infinite. 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 Star Fox 64 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.
Treasure's rail shooter, and the closest thing to a spiritual sequel.
The other great rail shooter, and visually still remarkable.
Rail shooting reduced to rhythm and light.
An indie game made explicitly to be Star Fox 64 again.
The most recent entry, if you can get on with the controls.
Arcade-length space missions with the same replay-for-medals structure.
Same era, same short-run arcade structure, same Nintendo speed.
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 Star Fox 64 that are not arcade games, so they are not on this page:
The full list is on games like Star Fox 64 — 9 picks, no genre filter.
Sin and Punishment: Star Successor. Treasure's rail shooter, and the closest thing to a spiritual sequel.
No. Star Fox 64 released on the Nintendo 64, 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 Star Fox 64 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.