The attacks they purposely chose to show in the video are common moves that could be learned by many Pokemon, so it doesn't matter that they're all normal moves. Now that we know the name in other languages we have more clues.
Japanese: Ninfia (Nymph - Greek for female nature spirits)
French: Nymphali (same Nymph as Japanese)
English/Spanish/Italian: Sylveon (Sylph - air elementals/winged fairies or Sylvan - of the woods, both from Latin silva "forest")
German: Feelinara (Fee - German for fairy)
This pretty much only leaves Flying or more unlikely, a new Fairy type. Yes, Normal does encompass some cute "fairy" Pokemon, but they would not make a Normal Eevee evolution because it goes against the entire theme of the Normal typed Eevee being able to evolve into other types.
Japanese: Ninfia (Nymph - Greek for female nature spirits)
French: Nymphali (same Nymph as Japanese)
English/Spanish/Italian: Sylveon (Sylph - air elementals/winged fairies or Sylvan - of the woods, both from Latin silva "forest")
German: Feelinara (Fee - German for fairy)
This pretty much only leaves Flying or more unlikely, a new Fairy type. Yes, Normal does encompass some cute "fairy" Pokemon, but they would not make a Normal Eevee evolution because it goes against the entire theme of the Normal typed Eevee being able to evolve into other types.