1) MGO is indeed a sponsor. It's like Team Dignitas, or TCM (Team CoolerMaster). Not sure if you know any of those, they're pretty known in Europe. They sponsor their team with servers and mumble (that is what we got from DAKKA), and better MGO's like the one I mentioned above sponsor top teams and they also give them LAN support (which means they get free shirts, and they pay the teamplayers costs for going to LAN).
Some sponsors even give some kind of payment if their team ends in a good place like top 3 or something.
2) What they mean with 'let go of their previous TF2 team' is that their previous TF2 team wasn't really playing anymore. That team had some problems and doesn't even exist anymore now. So with let go they mean they stop sponsoring the team because it's not performing anymore or even close to death