To make it / have made it = to complete some task or action. So in this context he “ would have made it into the bathroom “ would have gotten there just in time …to lock the door and to use the toilet ( I presume)

When something comes from the outside to inside = get INTO ( enter) If something or someone is sitting out( usually something) that means they are not taking part in something or it is stationery or inactive.

It is a 3rd conditional clause, so...let's paraphrase it... If someone hadn't put the board game there (in front of him as an obstacle), he would have entered the bathroom safely.

FYI, MADE IT TO is more common. MAKE/MADE in this usages basically means, 'manage to get to'. Some examples would be: We made it to the airport just in time to catch our flight. I made it home in time for dinner. I hope to make it to France for Summer vacation. Hopefully that gives you an idea. In this case it uses INTO because the person is going into a room.

Made into means he going into so he would have gone inside the bathroom. and sitting out means something was left out or put down somewhere.