This is such a silly argument. I ran through MGS3 without doing any stealth, just running and gunning. Is MGS3 now no longer a stealth game because stealth is merely a mechanic in an arsenal of tools? Absolutely not. Whether its the games primary gameplay mechanic or not (and again note how it very well could be) is irrelevant if its included in as a gameplay mechanic. You could play TLOU just as much as a cover based shooter as you could with gears. The fact gears came out seven years prior and managed to, at the time, perfect cover shooting while TLOU lagged so far behind thereafter is a negative on the gameplay experience.It's a mechanic in an arsenal of tools. It's no more a cover shooter than MGS4 is. Just because you can hug a wall and shoot from behind it doesn't make it like Gears where it is the primary, essential and arguably only mechanic.
Further to that, neither Joel or Ellie are meant to be highly skilled military operatives. They aren't supposed to be shooting from cover to cover with roadie runs, headshotting and decimating hoardes of enemies. It is a game designed to make you feel like every fight is a resource limited scrap for survival and it is effective at it
The second part means nothing to me because again, you very well could run through the game like that if you were skilled enough and essentially make them highly skilled military operatives. Your entire argument is predicated on the idea that because the game offers alternatives to playstyles that the playstyles in question get a pass for not being as fluid or up to date as games that have done it better several years prior to the game releasing. Which is silly, if you include a mechanic in your game, I'm going to evaluate it as a mechanic based on other systems with similar mechanics-regardless of alternative playstyles. And in that regard, it felt antiquated and why many people bring up gameplay as a weakness of the title. Others might not feel that way and thats fine. But it certainly doesn't get a pass from criticism because of alternative playstyles. If you feel that way by all means but I'm not going to keep arguing about it because frankly I find that to be an absurd position to take.