So...how many do we have?

129 MLB signees is correct. This is the # of players who signed professional contracts, not those who made it to the Major Leagues.

When you get drafted you sign your contract with the MLB team, then you get assigned to a location. I guess its all in the verbiage, technically we have signed 129 MLB contracts but dont have 129 MLB players.

You could add a lot more to the list of you called it MLB draftees and counted kids who got drafted out of high school and then attended and played at Ohio, then didnt get drafted after college because Carbone screwed their careers. I can think of 5 right off the top of my head.