I voted no on the Metal Slug X TAS, because I cannot accept continues being used in an arcade game, especially not a shmup or run'n'gun, because the entire arcade community agrees that if you didn't one credit clear, you didn't beat the game (alright, two players, so two credits, but you know what I mean). Finite reseources versus infinite resources, yeah. By and large, I agree with moozooh. But it's also a case-by-case thing.
Now, take the Ufouria TAS. The reason I pick that is a) because I console speedrun it myself and b) because it was the only one that came to mind. It uses deathwarping. You have no lives - dying and then hitting Continue means you're put at the location where you begin the game, but you have all the items you had when you died. Lives were turned into an infinite resource, used a lot, and you could easily make a case for that being Game Over. That was a TAS I had been anxiously awaiting, and when it was submitted, I was the first person to happily vote yes.
Hypocritical? Maybe.
But to me, continues in arcade games and console games are slightly different. Arcade games, especially run'n'guns and shmups, are by design short(-ish) games, made to hate and kill you, so that you spend a lot of quarters to get to the end, and this is also why most games (again, I'm largely from a shmup and run'n'gun mindset here) respawns you at the same point when you continue. And in an arcade, you actively compete with other players by way of the high score table, and as was previously mentioned, a lot of arcade games add a 1 at the end of your score when you use a continue (and oftentimes clears the rest of the score), as a mark of shame, and points out the score as not having been attained "fairly", in lack of a better word.
Console games don't work like that. There's no money. Most games put you back at the start of the current stage, or even the current "world" when you continue, and some do it when you die. They're made with a different mindset entirely. Game Overs usually cost a lot of time, you go to a game over screen, you have to start over from some point...
And I think that it's here, somewhere, that I can accept continuing in console games in a different way. In arcade games, using continues serve as nothing but to make lives an infinite resource, to gain a little time on the very screen it's used. And to get powerups from nowhere. In console games, using a Game Over to save time is only done when there's a VERY GOOD REASON to do so, such as aforementioned death warping or glitching.