Well… One can look at it this way, but this is mostly Google vs. Facebook. While FB + Skype is important I don't think Apple is really trying to get into social networks with Twitter integration. Honestly, I have no idea why they did it. Google and Facebook make money from advertising, Apple makes money from selling hardware (and a bit from selling content).
Apple needs applications clients want/need to use. Facetime is a direct competitor to Skype. Twitter integration will help on their social front. This is a 3-way war.