Condensation between chair mat and rug in basement: a concern?
Unfortunately, unsealed concrete slabs are fairly water-permeable, so the moisture level in the concrete will be pretty high. Until now the moisture has wicked through the rug and evaporated into the air, but it's now building up under the mat. Having the heating pipes in the concrete makes it worse, evaporating the water up through the rug; since the mat is cooled by the (cooler) basement air the water condenses on it.
Having a water-saturated rug, especially one that's warmed by the heating system, is asking for trouble.
Pulling up the rug and adding a waterproof layer would likely help, but that may not be in the cards; for now remove the mat and accept that the chair may damage the rug.