Master Labyrinth could be seen as something of a competitive tile-laying game. The difference is that the tiles are already there when the game starts, and the players push them around on the board, making and breaking pathways in the process. The changes the board can undergo in just one turn can alarm, delight or frustrate, depending on if it helped or hindered the path to your destination.
The aim is to collect ingredient tokens, in numeric order, all the while trying to keep your opponents from doing the same. In addition, three of the ingredients belong to a special recipe - a secret goal card you get at the start of the game, different for each player - and are worth big points if you get them. You also get three wands that you can spend to give yourself another turn right away - useful if the next number is on your secret ingredient list and you need two turns to get there.
If you miss out on an ingredient for your secret recipe, the rules allow players to trade route information for tokens or wands. In practice, I find that this rule is never invoked.
The game plays satisfactorily with two players but it can get a bit slow at times because one player is essentially just trying to counter the other and prevent them from getting the next token. It plays much better with three.