Curious as to how people consider it. Also does you're answer depends on if there was any continuity between ancient and modern boxing? (generally there isn't considered to be, but some people here have made a case for it)
Personally I do, even if boxing died out,it certainly seems modern boxing was done with knowledge of the ancient sport. As for if it died out or continued to some extent, I doubt we can ever know.. We're never going to have enough evidence to show it didn't die out, especially in the early middle ages, and it's basically impossible to prove it wasn't going on. We know it was happening a while before we have any vaguely good records of it, and sports done by peasants wouldn't be expected to be well recorded at all.
Ancient Roman boxing used the chestus. I doubt that any fighter's "prime" lasted more than a couple of years. I'm not sure what the ruleset for ancient Greek boxing was. Some of those guys sound like they'd be pretty good.
Cestus fighting, Bareknuckle and Queensberry boxing are like Islam, Christianity and Judaism. Though we may try to divide ourselves for some unknown bigoted reason, in reality we are all of Abrahamic religion and all worship the same God (beating the **** out of people with primarily fists) So yeah I think ancient and modern boxing are all under the scope of boxing.
No. The ancient stuff has always seemed like a different form of fighting-based competition to me. Sort of a primitive, long-extinct evolutionary cousin, like homo floresiensis.