The get up is an amazing exercise. As coach said, it works pretty much everything and exposes weaknesses as well. So yes, stabilizer muscles get stronger. It is also great for strength endurance and skeletal muscular strength.
I do disagree that it is not a pure strength move. It's certainly not a power move like the clean and jerk or something. But see how long it takes you to work up to 10 solid minutes of getups with an 88 pound bell. You can't do that without serious strength.