Semicolons appear in long, complex sentences — they’re a hallmark of writing that would likely earn the tl;dr label. I can’t think of another acronym or initialism that includes a semicolon (or any other punctuation mark), so whoever included the first semicolon in tl;dr was bucking abbreviation conventions. He or she took an abbreviation meant to endorse brevity and made it longer and more complex by adding a semicolon.
Some people have speculated that programmers put the semicolon there because some programming languages end lines with semicolons. Others have pointed out that using the semicolon is grammatically correct because if you were to write tl;dr as a sentence, it is two clauses that could be properly joined by a semicolon. But, if you view the semicolon as a symbol of long, perhaps pedantic writing, it would be funny to include the semicolon in the barb you’re directing at writers of such works—ironic because it’s the opposite of what you would expect in an abbreviation.
Although “too long; didn’t read” seems to lack something, complete sentence-wise.
Still, it’s true, you don’t see punctuation in most such constructions, except for the exclamation point — see, for instance, OMGWTFBBQ!!1!