“Why do we care which side wins?”
Because of geopolitics. The Obama administration sees Russia as a prime strategic threat. Anything that diminishes Russia is good. Anything that enhances Russian influence is bad.
Same thing happened in Afghanistan. The Saudis, with US support, recruited, trained, armed Jihadists from all over the world to come and fight the USSR. So now we are supporting the Saudi proxies in Syria, to fight Russia’s ally Assad.
So why do we want the Saudis to win?