Mind if I try and think up some potential games?
-Competitive arena fight where each player picks a set of movement abilities to explore the world for loot to help them fight others/access more of the map for better loot.
-Cooperative tower defence-ish game where players start at a fixed point of interest and must defend it from monsters that spawn at other nearby fixed points. Area is slowly claimed by the players, allowing for new weapons/buildable-structures/materials/classes/etc. to be found and used.
-PvP Team-based land claiming game. Each team tries to access and destroy the other team's bases, and the last one with a base wins. Tiles could be claimable for each team, usable for gathering resources, placing/using helpful structures, etc. Certain points of interest could be claimable as bases, while others would be mini-bases, controlling nearby land for one's team.
-Battleship-esque PVP where each player picks 2 or 3 tiles on the map for use as their own personal base. They can respawn/heal at any of their bases, and to defeat a player, one must destroy all their bases. However, which tiles are bases are hidden from all other players, and must be searched for by other players. Tiles chosen as bases affect one's move pool, and moves might weaken as one loses their bases.