I think it's less the "story" and more the performances and atmosphere that sell it the most. Are there better stories? Sure, but is this one told extremely well? Yes.

Just watch the cutscenes on youtube

I half agree. I think that the story when taken as just a concept, or a pitch, is pretty basic and generic, it's not bad, but nothing I haven't seen before. However, it's the execution of that story that makes it so incredible. I personally have a lot of stories in games that I find more appealing than this one, but very few can claim to do what TLOU pulled off with its amazing voice performances, visuals, dialogue and direction. Most games with great stories that I can think of are limited by the technology of their time, or by the budget that they have, but TLOU was, arguably, the first real Hollywood level video game in terms of not just the story itself being movie quality, but also in having the budget and technology to make the vision that the creatives had for it a reality. Most games that I can think of that surpass TLOU in terms of story either came after it and were clearly inspired by it (like GOW2018 and Ghost of Tsushima), were released very long ago and hence didn't have the necessary technology to fully realize their visions (like the Silent Hill and the Metal Gear series), or they simply don't have the budget to do what TLOU did (mainly indie games like To The Moon and Omori).