Guess you didn't try it long enough. There's over 600 games on that list so I doubt you saw everything. It has a majority of the big named exclusives and a ton of PS3 multiplats. You'd have to get very specific to name more than ten games that it's missing. You act as if there's just a handful when nearly 700 games which should be well over half the games on PS3. Though I am curious, what is this big list you have of games PSNow is missing?I just tried PS Now trail yesterday, and the collection of games is crap, frankly, its not even an argument wort making. Regardless of whether or not PS1 games arent considered a part of PS2s library, the vast majority work. So its basically PS2 & PS1 vs PS4 and the handful of PS1/2 ports. If PS Now put every PS3 game up, it might be worth arguing.
But that's besides the point. When you search "PS2 games list" on any search engine or catalog, PS1 will not be a part of that. The question isn't "what games playable on PS2 vs PS4," but which library has the better games, which means PS2 vs PS4 games.