Alain and Tyson already won a league
They both won the regional league which isn't as big of an accomplishment in the grand scheme of things. The regional leagues are often held and the winners of the same go on to take part in the Champions League ("According to Cynthia"). This probably refers to the Post Elite Four/ Regional Champion challenge. While Alain and Tyson did win their respective regional leagues, they weren't the regional champions.
No, he is still the champion of Kanto.
They actually refer to him as an elite four member in Journeys. That said, the whole thing is silly because if Lance in theory is the second strongest trainer in the world, one would wonder who he lost his title to as that person would take up this spot.
Considering how the anime was open to Making Iris the Champion because of the games, I don't see why Gary couldn't be one. Iris was inferior to a very incompetent version of Ash and still went on to be Champion. Gary despite retiring from battling to pursue research, still managed to defeat Post Battle Frontier Ash. Gary could very well be a Top Researcher / Champion.
I mean,
1) Steven is a Regional Champion and the guy likes digging for Rocks.
2) Cynthia also spends more time exploring ruins, studying history, etc.
3) Even in the anime, Diantha is a famous movie star.
So considering how Blue/(The in-game Gary) is the Kanto champion in the games, it wouldn't be too much of a stretch if they show that Gary along with his research, kept up with his training and is now Kanto's strongest trainer.
Maybe he can be the 8th strongest trainer in the PWC and Ash can defeat Gary and take his place in the Master Class.