Anti-static mat connected to earth directly or 1E6 ohm resistor?
You (and the some of the other answers) focus too much on the actual value of the resistance to ground; the fact is that the actual value is irrelevant regarding ESD. The ESD charge just needs a path. If that path is high-ohmic (few mega-ohms) it will only take slightly longer for the charge to find its way to ground. But it will still be a fraction of a second which is still fast enough.

What is important is your safety. You do not want a large enough current to flow through your body when you inadvertently touch a mains live voltage! That is why the 1 Mohm resistor is important in the wrist-strap, but also in the ESD mat as your hand might be resting on it. What if your hand was close to the earthing connection of the mat and you touched a live voltage? Then that 1 Mohm resistor will limit the current, and you will only feel a slight "tingle".