At the end of Season 2, Genki is upset to find himself transported back to what he calls "the real world" after the Phoenix destroys Moo's body. Apparently his transportation to Pangaea was a magical call from the land itself in its time of need, much like when kids are transported to the land of Narnia in that series.
Genki is once again shown living his day-to-day life on Earth at the beginning of Season 3. Though not quite as boring as he had imagined it in his dreams in Episode 8, Genki still longs to return to Pangaea. He begins seeing visions of Mocchi that no one else can see, and follows them into a portal that returns him to the world of Monster Rancher.
As in most stories of this nature, Earth is depicted as a world devoid of magic and dependant upon technology. Though nowhere near as advanced as some of the ancient Pangaean civilizations, the people of Earth do participate in videogame tournaments and believe that the world of Monster Rancher is just a place of fiction.
Though we know Genki lives in a city called Allenville on Earth, it is never stated exactly where this is located, but it is assumed to be a city in Japan.