He's the sole surviving brother of the last monarch.
Let's be clear. For ANY of the existing candidates, their claim is only as valid as others want it to be. The Targaryans were overthrown (and notice that most of the people of the Seven Kingdoms don't actually want them back), Robert had no living legitimate heirs, and Cersei is .. well, Cersei. Not counting war, the legitimacy of any candidate is going to be because the remaining nobles get together and decide that this is the person they can live with the easiest. By that metric, Tyrion's claim isn't that bad. I could see him being a very valid compromise candidate.