Hmmmm.
The Russians' ship building industry is in such bad shape that they had to go to France to get an amphibious assault ship built. The proposed carrier is significantly larger and would be FAR more complex than the Mistral class LHDs. It's likely that pigs will fly before the Russians (re)generate the capability to build a ship of this size and complexity. And then there's the matter of a true carrier capable aircraft to put on whatever ship they build. The Su-27K/Su-33 had enlarged folding wings and tail and a tail hook, but did not have a launch bar on the nose gear. It must take off using only its own power. The MiG-29K has the same limitation.
And the released design of the carrier is self contradictory. It has a ski jump at the bow and the waist, but claims to have catapults. Catapults and ski jumps are (generally) mutually exclusive. This looks like vapor ware to me.