I'll make my case this way: Jak II, whether you call it a platformer or not, is born from the tradition of platformers, and retains numerous elements of that world -- the control, the goofy characters, the kiddy playfulness, etc. So as an evolution of that genre, it does an outstanding job in catching, keeping, and generating my interest. When I'm at my most ADD, this game grabs my attention. When I'm totally mellow and not distractable at all, the variety of missions, and the level of the challenge (it's hard but not brutal, which is the perfect pitch for me) pull at my thumbs.
If I look at the game as an action game, or as an adventure game, it's stunningly good, fat with great shooting levels, vehicle jacking, hovercraft missions, and some superb racing courses. Of course, the story is what drives this game forward, but it's the perfect blend of platforming elements and action-shooting that are so good, feel so right -- and with guns that feel so good -- that in the end, I don't give a damn what genre this game actually falls under. What is it? It's one of the very best games on PS2.