OK, I hope I get all of this correct but don't confuse having a NFL contract with being on the active gameday roster. There is a NFL roster and a practice squad. These are they guys with an active NFL contract who can be placed on the active roster on gameday.
Then there is a gameday "active" roster and an "inactive" roster made only of the guys on the above roster.
The gameday active roster is 46 players. This is set a few hours before the game. They set 46 players who are allowed to play in the game out of the 53 players on the NFL roster. 7 guys on the NFL roster are put on the inactive roster What I was saying is Rourke will probably be one of those 7 guys. A new rule is that if you have a QB among these 7 guys then he can play in the game only if the quarterbacks on the active roster are all medically unable. There are, I think, 16 guys on the practice squad which makes the number of guys you can have under contract 69. But these guys are under different rules. Their minimum salaries are lower. They can't play in games unless moved to the 53 man NFL roster. A player on the practice squad had to be passed through waivers. The Jaguars were able to move Rourke up at their discretion but they had to place someone on the 53 man roster on waivers, either to move that guy to the practice squad to to release him.
Lawrence has some sort of knee injury. He said earlier in the week that he expects to play. Who knows, maybe there is an outside chance that he won't, but most likely, the Jaguars just considered it more important to have an emergency quarterback or be ready to have another guy as the backup should Lawrence tweak something in the next couple of days. If they put Rourke back on the practice squad when Lawrence is fully healthy then he'll go through waivers again.
I said that "the number of guys you can have under contract is 69" but it can actually be more than that. There is also the injured reserve roster. I don't know if there is a limit to the number tha you can have on it. But it can only be players that were on the roster when they became too injured to play and it has to be for a minimum number of weeks which I don't remember. These guys are paid under contract and the team protects their rights but they obviously cannot play in a game.