sanscript: I'm not saying it's all impossible, but obtaining those rights are next to impossible, especially when most early software were written in the US, and by law, no one can touch an IP for, was it 99 years (?), after the owner is dead.
Only 70 years after death in most European countries.
Although there are situations where circumstances or a skillful lawyer could get around that.
First, the copyright law is only for creative work. If you can somehow prove that the software in question is not unique and creative, you could remove its copyright status. I would assume that any Tetris clone that doesn't add anything to the original idea could be regarded that way. And in the specific case of Tetris, it came from the Soviet Union, which no longer exists, so that might in some cases create nice legal loopholes to go through.
Second, if you can somehow detach "art" from the "code", you might have a way to distribute stuff. There are differences in national legislations, so it doesn't work everywhere, but basically if you have computer code, it isn't art, unless it's being run and executed on a computer. So distributing source code might not violate copyright laws. There are some previously commercial games that are now available as freeware, but only as source code, not as executables. Also software like ScummVM kind of falls into this category, as there's no arts assets within ScummVM, only reprogrammed code.
Third, and this is like an unexplored territory, laws in most countries do allow quotations from creative work. A passage from a book, a part of the song, or a short clip of a movie is OK for reviewing purposes and such. Now I don't recall anyone using this in any legal controversy that I'm aware of, but you could do something like embed 1/10 of some game on your website and call it "interactive quote for review purposes". Then it's basically a random chance whether that will hold in court (hope you have a good lawyer!), but at least that would be backed by like 150 years of arts reviews of all kinds, so the other side would have a very challenging task to show that "interactive game reviews" are somehow different than let's say music album review broadcasts which play small samples from records.
Fourth, and this is a very challenging task, is to show that the terms of use in older software don't in any way prevent online distribution. At least most 8-bit and 16-bit games probably didn't mention anything about online distribution in the "EULA" or whatever equivalent of that (if any) came with the game media. But if you somehow build a system which reads data straight from the original floppys or something, and then run that embedded in your own website, that's not "an illegal copy" as technically speaking there is no copy. And if the "EULA" didn't mention anything about online or broadcasting (and you still have that expert lawyer), I think there's a small chance that you can be seen not breaking any laws in court.
I'm sure there are other cases too where you could get away with things using this or that special situation to justify your actions. Not sure if it's worth trying though, but I'm sure some people will do it anyway.