the moisture is coming from the ground. Venting would reduce this to an extent.
The ply wood probably is not the sole structure holding up the concrete, the beams are the main source. But, this is not saying that the ply wood is not an intrigal part.
What is the spacing of the beams? You migh consider thinking about shoring up the flooring by adding more beams or closer together. Unless the concete is reinforced with rebar, it could crumble into between the beams.