not by much, because even taken literally creating a game around the fact of beating up the odd member of a group isn't exactly what I'd consider a great pedagogical concept
For all of those reading that think this is ancient history; I'm 27 and went to school in a city more progressive and accepting than any in America.
No, the game itself it homophobic, and everyone who played it knew or was learning exactly what everyone meant by queer, and it certainly wasn't 'odd'.
I do not discount your experiences at all, homophobia was still prevalent in my elementary and middle school and I also graduated in a liberal state in 2008.
(I absolutely hate that this was ever the case! Wish I had a clue back then)
There was no literal gay element to the game (in our town) but it was still a very hateful name for the game. The message was clear: when you had the ball, you were "queer" and therefore the bad guy and so therefore everybody chased you.
That said, we typically called the game by other names. It had a different name in every town and neighborhood, it seemed. I think we only called it "smear the queer" when we were trying to explain it to kids from elsewhere... it was called "roughie-up" where we lived, but that was apparently hyperlocal, so if the kid was from out of town he might have known it as "smear the queer."
https://archive.org/details/BAR_19810115?q=%22Smear+the+Quee...
That's not the game were talking about.
That article claims the homophobic, ball-free game was new in 1981, the ball game seems to be well established in 1969: https://www.postandcourier.com/free-times/archives/smear-the....
I don't see any reason to believe that “queer” in the ballgame has any connection to homosexuality.
The term, particularly in the mood century, was absolutely used to describe gay people.
The pejorative use to refer to gay people wasn't the dominant use of the term until, well, quite late in the 20th Century, and the structure of the game makes it a whole lot less likely that the reference was a pejorative reference to a sexual minority rather than simply the odd man out.
It's kind of like if you someone argued that the “ball” in the name of association football was a reference to testicles and not the main piece of equipment in the game. Sure, the word also was used that way at the time, but it doesn't make as much sense in context as the alternative, and without some evidence beyond the mere existence of the sense of the word it's not a particularly compelling explanation.