So what you were describing was a parody of D&D? Because you literally described the core mechanics of Munchkin.
If the parody is the same, is it still a parody?
This may seem familiar ...
Any work that employs satire, irony, or sarcasm in a proper and correct fashion requires that some portion of the audience be confused, or even hurt, by the work. Because ambiguity is not a bug, but the central feature of any work that plays with or invokes satire and irony. Simply put, the possibility that the audience can misunderstand the message is necessary to the proper conveyance of the message. This ambiguity is not a bug - it is the distinguishing feature.
And since @GrimCo brought up Starship Troopers (and also @Remathilis )
The reason why fascism is antithetical to humor is because it is always already straddling the line of self-parody; satire simply points out that the appeal of fascism is indistinguishable from the innate ridiculousness of it, and the only followers it will have are those who are unable to get the joke.
There is a reason we have Poe's Law.
To move this to TTRPGs, I would make the following statement-
While Munchkin is a parody of D&D, it kinda also isn't in terms of effectiveness, because D&D itself can straddle that line.* When I think of a game that actually parodies and satirizes TTRPGs effectively, I think of the original Paranoia, which wasn't just a comedic game, it was a game that effectively satirized the norms and tropes of traditional TTRPG play.
*In GODS, DEMI-GODS AND HEROES it says that a forty-plus level character is ridiculous. In our game we have two characters that are at one thousand-plus level. This happened in “Armageddon,” a conflict between the gods and the characters. Of course, the characters won. What do you think about that?
-From the very first Sage Advice, Dragon Magazine, 1979.