The mechanics of the tiles are detailed in the Tumblr post I linked. Essentially you use WASD or the arrow keys to slide the player character into tiles. Doing so allows you to pickup items, attack enemies or trigger special effects (eg lightning storm). If you are not currently on a quest, a quest tile will spawn which once used gives you 30 seconds to complete a tasks. Completing quests is currently the only way to increase your score.
Rather long but hope that helps :D