It's just a match-3 (or more, IDK how hard it'll be to get matches)
The direction blocks fall depends on whether a row or column was switched to make the match.
Blocks will never fall into space that wasn't occupied by the matched blocks.
New blocks arrive in the empty space nearest to the center of the board.
I might also add Yoshi's Cookie-style line-sliding for lines shorter than their neighbors, but I'm not sure.