Andrew the Droid is a rotation puzzler, that is a game in which you solve puzzles mainly by rotating the game image. "Down" is always screen bottom, so rotating it means your character (the eponymous Andrew) falls to the new down. Each level has a green dot that opens a portal, so you must get to the dot, then to the portal through a combination of movement and rotation. Red dots are "gems" which you can try to snag for -- well, not points, but egoboo, I guess.
It's a nicely polished little puzzle game, and the fact that you gain powers (like left- and right-rotation and jumping) over the course of the game adds to a sense of progress. From a technical standpoint, it's interesting to see that rotation puzzlers are increasingly noticeable in Flash games; rotation is computationally expensive with bitmaps, but simple in a vector-based system like Flash.
No word yet as to whether Lucasfilm will sue over the use of its trademark on the word "droid".