I think there's just fundamentally different dimensions to the concept of dead, but I think the biggest one is more or less which direction the factors are pointed in, in terms of it's community. It's possible for a game that doesn't get new product to be building on a healthy community, but it's one of the things that attracts people, so that's a factor against the game being 'alive.'
In another sense, dead can also mean it's no longer a living thing, it's not changing-- inert in other words, 4e is like this for me because it's meta is calcified to more or less what we had in 2012 or so-- whenever the last 4e products released, we're not really talking about new classes or developments in 4e, or speculating about how new powers could finally make a class good or something.
But something like Pathfinder 1e 'continued' the life of 3.5, and I think the OSR basically cast resurrection... or at least made a wonderful undead monstrosity out of ye olde TSR DND.
The community around it is itself another factor, if there's a bunch of people playing it that's a point in favor of it not being dead, and if they're talking a lot about it meaning there's a real conversation about it, that's another point in it's favor.
Another thing for me is actually the game's ability to offer things in the context of whatever the current market is, part of why I considered my once-beloved 4e dead, was because as frustrated as I was with 5e-- I still didn't want to necessarily return to pre-streamline era, and it wasn't until PF2e that I had a game that gave me what 4e did alongside streamlining, and I recently had a friend confirm when I mentioned how I genuinely regretted switching to 5e they were adamant that they much preferred 5e to 4e, and 4e was their first RPG, so back then it wouldn't have gone very well to go back.
But then, with all of these factors... it's also interesting that for me 'dying' is a lot more useful than 'dead' because there's always going to be a small contingent of diehards for these big names, so I'm more interested in what happened to the rest of the playerbase, the hype, etc.