To my mind, the salient feature that
specifically distinguishes a tabletop RPG from other kinds of game is that it is (and
I quote myself)...
A game whose ruleset is partially unbounded due to some combination of (1) the fictional personas are not limited to the gameplay moves outlined in the rules, (2) the rules by definition include gameplay moves that intend to allow an effectively unlimited activity set, (3) the rules grant explicit or implicit permission to players to add to the ruleset. Restrictions on permissible declarations will follow from the implicit or explicit restrictions of the fiction (†), from the rules (††), or from the expectations of other players (†††).
The symbols enclosed in parentheses were footnotes that expanded on the final sentence, which I do not believe are pertinent enough to include here.
For instance, no matter how imaginatively one constructs one's open-world video game (and games such as Minecraft, Breath of the Wild, Baldur's Gate 3, or Tears of the Kingdom all rate highly on this score!), such a game is still bounded by its code. You can only ever do what the code allows you to do, no more, no less. Board games and card games, which are not meant to be played with a computer or console doing the heavy mechanical lifting, are even more restricted on this score.
As such,
clearly there is something about tabletop RPGs, where resolution of in-fiction activity (aka gameplay) is mediated both by the game's rules/mechanics and by the ability of the human participants to step beyond the bounds of the mechanics, that is simply unlike other kinds of game, such that it's not clear to me that ensuring this "unboundedness" in RPG gameplay can be achieved without at least some degree of "push your luck [gameplay] with improv prompts".
At the very least, it seems out of line to suggest that RPGs,
writ large, "should not" include such elements as part of their gameplay. Some games - ones that are quite well-thought in most RPG-ing circles - actually
revolve around just this sort of play.
For instance, as I understand it, in a game such as Apocalypse World, when a player invokes the game mechanics of a Move and rolls badly, thus obliging the MC - what that game calls GMs - to make their own Move in response, the MC
is not expected to know ahead of time what Move they will make - and not only that, in fact: it would contravene the principles of how the MC role works in that game for them to pre-prepare such responses! (The perspective of someone more familiar with PbtA games would be appreciated here.)
As another example, Dread. While the game doesn't use dice, it undoubtedly does use "push your luck" mechanics in a very open-ended way that, dare I say, involves a great deal of improv from both the players and the GM-player (the "host" as the game refers to the role).