Your suspicions are very, very likely on the mark, but the only way to really confirm it are have an electronic leak detector company who specializes in vinyl liner leaks run a test on your pool. That'll cost $100-$200. Or the cheap way is to stop refilling your pool and let it leak until it stops. Wherever the leaking stops, your leak is at that point, somewhere along the waterline (shut off your equipment when it reaches the bottom of the skimmer)
There's a small chance they could fix it by applying some silicone to the wrinkled area in the step gasket but more realistically they'll have to remove the liner and have it sent back to the factory to replace the step area (along with all of the other cut-outs in your liner) and then re-install it correctly. Or just put a whole new liner in.
The photos show that it was a very poor install in the step gasket area. How does the rest of the liner look on the install?