It's not the normal thing to do, but it can be played with a keyboard. It's not so easy to just explain, you kinda have to play it well on a stick to understand, but the motions that you do to play really fast feel much more natural on a stick. I originally used the stick just because it was more fun (and because it's an arcade game), but now I can't play without it (and I have never played Puyo Puyo with anything else either, except the ones on the PSP). Besides, I have played this game for a few years using my stick. The keyboard could even be better as far as I know, same as in fighting games (keyboards could even objectively be the best way to play those, at least to me using a keyboard seems to give you more accurate inputs), but to me it just feels wrong anyway, and I don't think it's advantageous for this game.
I tried playing a bunch of games using a keyboard, and I thought it was actually easier to do even something like a spinning piledriver with Zangief in SF2, just because the keyboard makes your inputs so precise (and in that case it's a lot more forgiving in general), and I had no practice using the keyboard at all. I still use the stick for everything regardless, because using a keyboard is just weird, and the game wasn't made for that so it could technically even be cheating (you can do some really retarded bullshit in SF2 if you use a keyboard). In TGM, I don't think it matters. If it's a 4-way stick, I think it should at least be as good as a keyboard. In my case, I am handicapped because I don't have one of those. My stick is for everything, not just games that benefit from that. It's a lot harder to not mess up, though. I consistently get to the 900s and lose. Still, it's not like I can't just improve even more so I mess up even less. Might benefit me in the long run.