It does seem to be working. The white/gray check pattern in MV means it's transparent. It will be transparent in game, it just appears that way in the engine to make it easier to see what is transparent.
If you want to try changing the transparency in MV, I made some screenshots to show you how. This can help you identify the transparency better. I make mine a birght pink so I can tell where it is. Hope that helps!
It looks like the transparency is there fine, just as MushroomCake28stated.
If there's nothing underneath it will be black. Think of it like there's a black canvas and you start painting on it with tiles. If you have a 100% transparent tile, and if you put nothing else underneath it or on top of it, you'll just get some black.
You can see that there's nothing underneath the table since you can see the editor's transparent marker (the white and gray check pattern). You need to place the floor tile first, then place the table tiles on top of it. If you've set your tileset correctly, it should work and the table should be on top of the floor. If you didn't configure your tileset correctly, the table tile could override the floor tile, which is one possible explanation to your problem.
Floors override each other, but you can place walls and fences/tables on top of floors. The way the system determine what type is a tile is by looking at its position in the tilesets. Head over to the database and in the tilesets tab.
Tile A1: All animated floor tiles (usually water tiles)
Tile A2: The first half vertically is for floor tiles (ground floor usually). The second half vertically is for anything that goes on top of floors (grass, fences, tables, holes, etc.).
Tile A3: Walls and Roof
Tile A4: Walls
Tile A5: Miscellaneous
A1 And the first half of A2 can't be on top of each other.
The rest can go on top of A1 and the first half of A2.
I didn't know that A2 is split-up into two different tile-types. I guess this should solve my problem. Is it pre-defined in the system that the second half of A2 begins after 384 pixels and ends after 768 pixels?
I hate seeing threads where less-experienced user's ask for an opinion of their project, and the thread is full of negative feedback by others who are clearly not the target audience. I feel bad for the OP, and I hope they understand that no game can appeal to everyone.