You could analyze pipes and wiring, looking for things unaccounted for in the rest of the house. But the only way to know for sure is if you open a hole and have a look.
If the lower floor is "half-underground" it would be fairly unusual to have no room there if the ground is level and "halfway" all around. If the "mystery room" side is uphill and fully or near fully underground, while the other side is fully or near fully exposed on the downhill side (thus still allowing for a description of "half-bured") you are probably going to be disappointed in your "mystery room", as it is very common to have a step-wise foundation in that case, and the area will very likely be full of dirt, probably with drywall over studs over concrete wall, from the description.
I managed to find a "mystery cubbyhole" in my abode once by noting that measurements didn't add up. Nothing exciting in there, just a "dead space" (per the thinking of builders who didn't believe in storage space, I guess) covered in drywall and closed off. After scratching my head a lot and triple-checking how the measurements didn't add up, I cut out an access hole in the drywall between two studs, and there it was. I also lived for a while in a house with no mystery - there was a narrow, accessible space behind the uphill wall of the lowest room, and the wall behind the wall was raw rock that the foundation had been quarried into, which leaked out water when it rained. The non-mystery space was there to divert the water into a drain.