Yes it is. As mentioned in the description its because of the Coriolis effect. I dont know to what extent it would affect balancing an egg, its not a huge force but its plausible. Btw: As mentioned in the comments the water experiment is probably not entirely fair because the equipment is not build accuretly enough but in essence yes, it does happen.
lol another fun-fact. The spinning gyroscpe has its own will and will not fall the ground as gravity says it shall! http://www.youtube.com/watch?v=cquvA_IpEsA
Aight can we start using The Lounge for something else than posting videos regarding elementary physics?