Yes the tires have a bigger overall diameter (i don't remember exactly how much it is, I'll check) and they are wider too (205 wide) but what makes it look so big is that they are much "rounder" on the tirewall. Road tires have a pretty straight tirewall, so it's kind of "flat". These are more like racing slicks (logical as they are remanufactured and grooved slicks).
The car is lowered a lot. The ground clearance must not be much less than stock as the wheels are bigger so it counteracts the lowering, but as you can see when the car is up in the air, the gap between tire and wheelarch is very small. I've never measured (would have to compare with a stock RS) but I'm guessing around 6cm drop. I used to be lower with the 15", and had to raise it to avoid scratching everywhere in the wheelarches...
But with the new engine will come new axles and spindles from Clio/Megane, and the car will be much lower (aiming at 6-7cm off the ground). But then it will be a track car only, no more road use, and definitely no more daily driving.