ESD mats may very well only start leaking current at higher voltages, and it may be "open" to a DMM even if it can measure to 100MOhm.
Testing ESD mats is usually done with "Isolation testers" which generate 1000V or more.
In the "ugly outside world" lots of things that seem simple are not well modelled by lineair things such as resistors. Take for example a "spark gap". At low voltages, it's just an open connection, but above some threshold you get a spark and during a brief moment resistance is very low.
As far as I know, the plastic polymers in ESD mats are a bit like varistors. Below their threshold voltage there is virtually no current.
Calibrated ESD mat testers are overly complex and expensive. There are test procedures wich specify test contact area with the mat, and test weights or pressure on the mat to get a calibrated measurement.
But if you make a (somewhat calibrated) 1000V generator, add a few series resistors to keep the current low (and make it safe), then you can easily measure the voltage over one of shunt resistors (Resistors are usually rated for 200V or so) to get an estimation of the mat resistance.
One of the "dangers" with ESD mats is the wrong kind of cleaning substance. Some may leave a very thin but isolating film over the mat.
For the wristwrap it's easier. Your DMM indeed probably measures some resistance between your hand and mans earth (if your wrist wrap is properly connected).