It can be real. Just add a motor with a fan in the back.
Your arms and legs can still do all the steering and altitude control (which is where the fun lies).
It's the flapping that is impossible. It's so incredibly clear than the kind of flapping shown in the video can not provide lift (no matter how strong your motor, and no matter how large the wings) that I don't understand how anyone was fooled for even a second.
If you want to flap then on each upstroke you have to either fold the wing or rotate it. Otherwise you get nothing except an up-and-down bobbing.
If you ever get a chance to hold a bird extend its wings and look at the construction and the way it moves. Notice especially the "elbow" in the middle of the wing.
Every time I launch into the endless blue, unpowered, under a wing comprised entirely of what was just a crumpled mess of fabric just moments before, it's real for me.
Besides, why bother with flapping when you can soar and thermal? ;)