The gamer series takes a different route from the anime during/after the fight with Heathecliff. The first game (Re:Hollow) plays from floor 76 and up. Lost Song is a completely new story that takes place in ALO after the first game. (It's better than the anime fairy arc imo for various reasons) The 3rd game.... I'm about to find out. Enjoyment wise, Lost song is very fun for gameplay and co-op missions. (They don't affect main game other than a good way to power level) Re:Hollow had some pretty complex mechanics that it rushes to teach you and is like an anime visual novel most of the time.

What kind of games are they? I'm guessing rpg, but what kind? Is there a lot of loot to collect and levels to gain or anything?

Yes, RPG. A lot of quests and grinding type.