It's not just Tetris you can recreate. Another of the four games is clearly based on Columns, except instead of matching three of the same coloured gems (or blocks as they are here), you have to match five. The default Tetris is also a bit weird, as the scarcity of column blocks means you don't often get the satisfaction of stacking 'em high and then watching 'em fall.
So Block Factory is lacking in identity, then, and by calling the preset games Game 1, Game 2, Game 3 and Game 4 (Tetris is Game 1) it's almost as if Enjoy Gaming know it. Still, they'd hope that the level editor would make up for a lack of originality.
The effort has been put in here - it's very easy to make your own Tetris clone by selecting different blocks and a background with the stylus before sharing it with friends via StreetPass or QR codes.
In Pullblox we can see why your friends would want to play a puzzle you've created that looks like a Pokémon but as we said at the beginning, will they be willing to play a Tetris or Columns clone? At £3.60 it's pretty good value, but that's the best thing you can say about it.