In other words, the water has nowhere to go.
Looks to me like the living chamber is pressurized to match the ambient water pressure, so realistically a free diver could enter but would still have the same limited "bottom-time" as when they are using scuba at that depth, otherwise the same decompression regime would be required upon ascent.
The conditioning of air for a relatively closed system should not be expected to resemble or contain the same elements as an ordinary residential application where cooling is the main consideration and moisture removal is a side-effect of the most common apparatus in humid environments.
A regenerative industrial air-drying unit could be adapted, at least I know I could do it, but may not be within their energy budget.