The best indie games like Mike Tyson's Punch-Out are Sifu, Absolver and Furi. Below are 5, each with the reason it is here — and, at the end, what filtering to indie costs you.
Filtering to indie means you want the answer a small team would give. It is usually the most interesting filter on this site, because small studios take the risks large ones cannot.
What you get: One strong idea, explored completely, at a price that makes trying it easy. Indies have no production to hide behind, so the design is exposed.
What made Mike Tyson's Punch-Out worth playing in the first place is covered on the full list. This page is the indie part of that answer, and only the indie part.
A whole game about learning one opponent's tells and executing perfectly.
Martial arts as pattern reading rather than button mashing.
Boss-rush only, and every fight is a memorised pattern.
The purest modern boss-pattern game, and just as unforgiving.
Reduced to nothing but timed reactions, and it is superb at it.
Polish and scale, sometimes. A few of these are rough at the edges, and a big-budget pick will always look better doing the same thing.
Specifically, these are strong answers for Mike Tyson's Punch-Out that are not indie games, so they are not on this page:
The full list is on games like Mike Tyson's Punch-Out — 9 picks, no genre filter.
Sifu. A whole game about learning one opponent's tells and executing perfectly.
No. Mike Tyson's Punch-Out released on the Nintendo Entertainment System, 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.
Self-published, or published without a large publisher's money. It says nothing about the size of the game, which is why a forty-hour metroidvania and a two-hour art piece sit under the same label.
Constraint. Without a budget to hide behind, one idea has to carry the whole thing — and a small team can commit to something risky that a large one would sand down.
By hand. Each pick was written for the full Mike Tyson's Punch-Out list first, on what the game actually does, and this page is the part of that list that is indie — 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 indie guide for where to start in the genre generally.