What makes Tri Attack a Normal move? What makes Pursuit a Dark move? Same with Beat Up. What makes Mega Punch a Normal move? What makes Cut a Normal move but Fury Cutter and X-Scissor Bug moves?
...we could probably play this game for awhile.
I can answer Beat Up. Most Dark type moves are underhanded and dirty ways of fighting. Ganging up on your opponent to beat him/her up is not a very honorable move, now is it?
And Tri Attack, well, it would be like 3 types at once, so they went with the type that represents neutrality, I think.
Alright, Beat Up is the most readily explained, but Tri Attack is not explainable by types. We knew they were thinking of 'canceling' them all out, but we don't see that anywhere else in the franchise that I can think of. I suppose Lugia may have represented the same concept in the second movie.
Go to Gamestop, buy a Steam card, and use it to purchase Ys Origin. You won't be disappointed. Don't reboot PCs that you cannot access.