In general, water shouldn't be getting through tile or linoleum or whatever's installed as the flooring in a room like this. However, some cracks and pores might eventually come to exist, which is why waterproofing is necessary for the subfloor. Where it goes depends on what's going on in the room: if the flooring is sloped towards a drain, it'll go down towards the drain. In the video you linked, the baseboard area is waterproofed, and there is a drain in the center of the room, so if you had a large amount of water pouring in, that's where the vast majority of it would go.
Usually, though, we are talking about small amounts of water here. If a few droplets manage to get through some discontinuity in the grout or whatever and don't make it all the way to the drain, they'll eventually evaporate, and the water vapor will come out the same way the water got in (if water can get through cracks in a floor, so can air). Generally speaking, water doesn't stick around forever if it's exposed to air -- if you leave a glass of water on the counter and leave for a vacation, for example, you may well find that it's completely empty when you get back. An exception is if it manages to seep its way into a porous material, in which case it can stick around for quite some time.
Of course, "eventually" is relative. If you have a big crack in your bathroom tile, and it's right near the place you step out of the shower every day, it's possible that there will be some persistent wetness between the tile and the waterproofing, which could get to smelling rather bad, but it's not like it's going to stay there forever (if it got to be really awful you could just turn on a fan and open the windows or run a dehumidifier in the room).