For a cut-the-rope style game, GameMaker is probably the best style of game engine.
For a side scroller type game, Unity's 2D shows a lot of promise. You may or may not choose it after looking closely, but that is up to you.
They are right that the engine is still fundamentally 3D. The 2D is just a view along the Z axis, plus tools for sprites, sprite sheets, and sprite-based animations. The interesting thing about it is that the 2D and 3D components can live together. So if you want to throw a 3D thing into a sprite-based world you can do that.