From what I can see the inventors have used some very thorough research into how insects, particularly the Hawk Moth, generate lift using vortices on the leading edge of their wings. From this they have manufactured an intricate mechanism that can flap the wings in the exact same way, or very nearly. The wings themselves are made of stereolithography resin, and manufactured using plastic stereolithography to the same basic shape as an insect wing. Then a thin plastic membrane is glued to the wing ribs, what they call an "interstitial membrane", tisk, tisk, creating a wing that can beat the air. The powerplant is called a reciprocating chemical muscle, which appears to be composed of twin, opposed, metal pistons. Instead of combustion with the air, it uses a monopropellant that does not react with the atmosphere. My guess would be something like hydrogen peroxide fuel with a silver catalyst inside the pistons.

This appears to be the real deal folks! The proposed mars flyer would be about 3-feet across and carry a 30-pound payload. Here's more information, and a few really impressive videos too:

Space.com Article
Entomopter Description
Reciprocating Chemical Muscle, Graphs & Formulas