When you say 'range of motion', both a muaythai kick and a leg press have the same ROM...which is zero. Range of motion is determined by the final joint angle minus the initial joint angle, and since both movements are a cycle, you get zero. So maybe that's not the best vocabulary to use.
As far as 'the muscle responsible for stretching the leg', muscle is responsible for stretching the leg if the contraction is what is called an 'eccentric contraction' -- meaning the fibers lengthen during the contraction. You get this often when you are resisting gravity, like trying to maintain a moderate speed when running downhill. I'm not sure if this is what you are talking about?
Muay thai kicks follow the classic 'stretch-shortening cycle', where force is developed using eccentric contractions followed quickly by a concentric contraction. This is the same strategy you will spot in many high-power generation movements. As such, the hip flexors (illiopsoas) will contract but isn't a prime mover, as opposed to karate-type snap kicks that have a tremendous demand on the flexors. If anything, the posterior chain will contribute more during the preparation phase than the flexors on the anterior of the body, since that's when the GRF has time to develop, being that you are in double support.
I suspect the reason you are seeing more hypertrophy around the patella is because, if you knew it or not, you are now training for hypertrophy in a closed-chain movement. Your volume, intensity, speed, and recover time is now totally different than it was in muay thai.
- you are seated and aren't challenged for balance, like in kicking -- thus you can apply more force as you do a knee press.
- leg press is symmetric, meaning you can overload the muscles in the leg in a safer manner, which gravitates you towards moderate to high loads.
- leg press puts higher eccentric demand on the quad than you could ever get in muay thai, and it's the eccentric demand that leads to the hypertrophy you are noticing.