“So, here’s the issue: while it is demonstrably true that not everything that brings one profit is fun, is it similarly accurate to hold that fun is not always profitable?”

No.

With the prior understanding that “profit” isn’t always accrued monetarily where Fun is concerned... AND the understanding that “at someone else’s expense” doesn’t involve Fun – it seems to me the only fun one can achieve MUST be profitable.

“Fun” can result in financial, emotional, intellectual, physical, epistemological, even serendipitous, profit. “Profit” equals “gain”. As long as it doesn’t hurt or take from others, it can be viewed as a gain or a boon to the actor. As long as the "profit" was satisfactory to him during or on completion, it can be viewed as “fun.”

Except for serendipitous profit – which would seem to make Fun even more pleasurable – choices are involved in every act. When one acts on his choices and completes them, he can feel satisfied that his goals were correct, and that he is worthy of life itself.

Self-satisfaction is its own reward.

That would HAVE to be fun!