Okay, so I am going to vote for Latios for #2 most influential pokemon, but before I get to that, I'd like to address why I don't think that Tyranitar is a very good choice.
Tyranitar is a good pokemon. Fantastic, in fact. He's got a bunch of good sets he can run and is pretty clearly a top-tier threat...but this isn't about the best pokemon, this is the most influential. I think of "influential" meaning filling a unique role and forcing adaptations from the metagame in order to cope with the presence of a pokemon, and I don't think Tyranitar does that to the extent that others do. What does Tyranitar bring, on its own? The only role that Tyranitar and only Tyranitar fills is a powerful and bulky Pursuiter. In everything else, he has competition - Hippo as a defensive sand starter, Garchomp as a bulky offensive SR setter, Dragonite and more as a mixed lure, etc. Generally, Tyranitar is picked over one of these pokemon because of the extra, incidental benefit of sand. But as we all know, sand is not really an archetype on its own, but a reaction to the prevalence of Rain and Sun. The only dedicated sand teams (sand stall) almost universally use Hippowdon. In short, Tyranitar isn't an influence on the metagame, he's a reaction to the metagame. What does TTar influence? Well, Celebi runs Baton Pass and Latias/Starmie occasionally run Reflect Type. Other Psychic and Ghost types must be wary of being Pursuit trapped. But other than that, you don't really gameplan for Tyranitar - any other role that he fills is done just as well by something else that you're handling anyway. Meaning, if you can't handle Tyranitar's offensive presence, you're probably getting fucked by Terrakion anyway, etc. For that reason I wouldn't describe Tyranitar as influential to the metagame. An important component of it, but not something that changed it too much.
On the other hand, Latios brought a new breed of specially attacking power to the table for OU. For starters, every other top-tier Dragon type is pretty much always physically based. The only other one is Hydreigon, who has his own flaws. Meanwhile, Latios brings a metagame-defining 110 speed to the table (110 is a huge benchmark...mostly because of Latios) as well as a ridiculously powerful 130 base Special Attack. Latios marked the first time that the need for steel types extended to special walls, making more popular specially defensive Jirachi, Ferrothorn and Heatran. The additional wallbreaking power of STAB Psyshock and Trick made adaptation even more necessary, as sturdy special walls like the pink blobs, Rotom-W, Tentacruel, etc. no longer cut it. Also, Latios is pretty much the pinnacle of OU revenge killing, only recently challenged by Keldeo. The metagame reacts to Latios in a way that it doesn't to Tyranitar - it pushes the increased tempo of HO, prevalence of specially defensive steel types, and more specialized special walls - for those reasons, I'd call it the #2 most influential pokemon of BW.