It's no given that this will help a Big 12 team make the CFP, and it very well could hurt on average. It's amazing to me that the public at large is so scientifically and mathematically illiterate as to think that an analytics firm's statistical model on this question is by its very nature some sort of distillation of objective truth.
There's essentially no data to draw on (only two years of the CFP), and even if there were many more years, any model's results would
still rely very heavily on the underlying assumptions the modeler makes. As it stands now, the assumptions are virtually everything. Here, the firm's premises basically assume the truth of its conclusion: for their model to show that adding a championship game improves the conference's chances of landing a team in the playoff, given the paucity of actual data, this firm had to assume from the outset that the CFP committee was far more likely to favor teams from conferences with CCGs than ones from conferences without. So the Big 12 basically paid gobs of cash to an analytics firm to engage in circular reasoning and produce correspondingly useless conclusions.
Here's a quick rundown on the stupidity of all of this:
http://www.footballstudyhall.com/2016/5/17/11683756/big-12-expansion-championship-game-playoff-odds
The only thing our rematch-game CCG is guaranteed to do is provide a nice payday for the conference. (Of course, for the members most likely to make the playoffs, one loss that knocks a given team out of the CFP will probably end up reducing that program's revenue generation by an amount that offsets years of CCG payouts.)