It's hardly surprising the #1 most critically acclaimed PS1 game series also makes it into the PS2 list. Carrying on the pure skateboarding tradition of its predecessors, Tony Hawk's Pro Skater 4 continued to perfect the mechanics and level design set forth by the previous installments.
Pro Skater 4 was the last game in the series to bear that branding (ignoring the upcoming PS5) and be a skating simulator. The games that followed were very divisive and more GTA-inspired. Pro Skater 4, however, had excellent mechanics, impressive graphics, the always-awesome level design, and introduced multi-player into the series.