So you are aware... improv has rules.
People doing improv don't use dice to resolve actions, but Improv isn't "anything goes," kids playing cops-and-robbers either. Improv actors have guiding structures by which they operate, so that the result is coherent.
If there's an argument that improv isn't an RPG, it is in the fact that, usually, the actors actually do know the general plot of their scenario before they step onto the stage. They are improvising the details, but not the large-scale plot.
In a sense, everything has rules, and yes, you can look up improv rules and find a list that looks like this:
1) Say “yes’and!”
2) Add new information.
3) Don’t block.
4) Avoid asking questions- unless you’re also adding information.
5) Play in the present and use the moment.
6) Establish the location.
7) Be specific and provide colorful details.
8) Change, Change, Change!
9) For serious and emotional scenes, focus on characters and relationships.
10) For humorous scenes, take choices to the nth degree or focus on actions/objects.
But there's a pretty big difference between "Rules" in an RPG and "improv rules" -- or Chess rules, at the other end of the scale.
Chess has
strong rules. If you break a rule, you are no longer playing chess. If you are playing chess and decide to move your bishop horizontally, the game will stop and not continue.
RPGs have
medium rules -- they are rarely broken and if they are, it's often because a new rule supersedes an old one. If I want to go before an orc in initiative, I'd usually have to have a rule-based reason to do so. "Rule Zero" allows a GM to arbitrarily ignore rules, but even so, they rarely do so per se, it's almost always because of a rule that is hidden from the players' view.
Improv has
soft rules. If I don't "establish the location" or I block, it doesn't stop the improv -- people don't suddenly jump into a rules discussion like they would if you declared you were going before the orc. It just makes the event weaker and makes you look bad. It's advice or guidance, not rules. You could ignore all the listed "rules" and still be doing improv. You couldn't ignore all the rules in D&D and still say you were playing D&D.
For me, that's not equivalent to an RPG rules - Improv "rules" are more like a social contract. In fact, you could take most of the above improv advice and it would make a good social contract. So I'm not in agreement that you can compare the two.
As a minor detail, I have also seen a fair amount of improv where the actors have no idea of the general plot and do make up the entire story on the fly. Dropout has a whole series of musicals that are improv, and the cast create plots, characters, resolutions, locations, you name it.