All tetris games I've come across have this feature.
Not Tetris for Game Boy. Or Tetris for NES. They don't allow sliding tricks. And considering your game lacks a hard drop and wall kicks, I'd think that would be the style of game you're going for.
Edit: I prepared a three diagrams for you, since technically it LOOKS like the Game Boy and NES Tetris support sliding. The reason for this is that the blocks don't fall down smoothly. They go cell by cell. But code wise, the blocks are going pixel by pixel. That's how the falling is "timed". Look at this gif which shows how NES Tetris behaves. On the right it shows how things look. On the right is shows how things are done.

You'll notice that even though the left block is "touching" the bottom, it is still free to move because the right block has not hit the bottom yet. If this was not the case, it would be as if the block fell two cells instead of one when it touched the stack. This is NOT lock delay and no sliding is occurring. Only the block on the right matters. That might lead you to another observation. "Why don't let they us see it the way it is? That's dumb." The next gif should explain that. And it has to do with a move that looks like a slide. (but is not). Once again, the piece on the right is the way things are. On the left is the way things look. I added a pause where the piece "slides" in.

Notice how strange that looks on the right? The pieces are overlapping. That's why it's not displayed this way. Again no slide has occurred. The piece was just moved left before it actually touched the ground.
The next gif shows how Tetris for NES behaves and how your game behaves in one situation. I reported this as a bug in my own review, and I stand by that. The left two spaces are how Tetris NES behaves. The right two spaces are how your game seems to behave. I put a pause where lock delay begins for your game. Keep in mind Tetris NES does not have lock delay, so while the first t piece in your game's field is still active, another block is given to the spaces on the left. Both games get the same input for clarity.

This is what I meant in my review by you can lock a block in the air. This should not be possible. It should lock one block lower than it does in the gif. (And sometimes this DOES happen. But if you constantly "float" a block over a space, occasionally it will lock in the air like that. )
I also recommend checking out this link:
http://www.tetrisconcept.net/wiki/Lock_delay and reading some of the wiki there.
If you want
lock delay with
Game Boy or NES rotation, and no hard drop or
wall kicks that's fine. I'm just pointing out the fact that actual sliding is not possible in old Tetris games. One last thing, is that games that DO have lock delay usually have a way to cancel it and lock the piece so you don't have to wait for it every single time when you already have the piece in the right place. If you choose not to have that for your game, I agree it's your choice not to have such a mechanic, but it makes it less appealing to me.
I apologize soulanger for posting this here, but I am a big Tetris fan and I felt the need to cover this. If you dislike this, I will remove them.