This 3x3x7 is fully functional. It is cubic, meaning that it doesn't change shape as you solve it. It's about the same size as a 3x3x3 cube and looks and feels like the top and bottom layers have been sliced in three to make the extra layers. The thin layers behave a bit like a bandaged cube when the top and bottom layers are not solved.
The puzzle in the image is a Cube4You DIY. It is built around a normal 3x3x3 core. The centres screw into the core as normal. The thin layers stack on top of one another, the pieces fitting together to make a stack equivalent to a normal corner or edge. The puzzle fits together well and turns reasonably well. There are a lot of pieces in a small space so it's not really a speed cube.
Solving this puzzle takes a little longer than the 3x3x5 version. I solve the puzzle from the inner thin layers towards the outside, doing the middle layer somewhere near the end too. The increase in size doesn't really change the way you are solving the puzzle - reducing it to a series of Domino puzzles and then solving as a 3x3x3. In that respect, it's a little like the cubes larger than the Revenge - the scale adds time rather than difficulty to the solving.