I wish I could accomplish so little. :-)
Facebook connects people. Television can inform. Movies can inform.
Yes, video games are almost as useless, but at least the consumer is actively involved... I love sports when people play them. When they watch overpaid idiots play them and obsess about it? Not so much.
There are lots of examples of $company:$product pairings, e.g. Apple/iDevice, Google/Android, Microsoft/Windows.
Also, before you cast the "provide entertainment" stone, you should look around you at how people are using tech company products. I would venture to guess that, outside of the workplace (and inside the workplace when workers can get away with it), entertainment is the #1 use of computer-based devices. Apps in the App Store, game consoles, computer games, YouTube, emailing LoLcats, browser-based games (Farmville - 100% wasted time) etc.
As you said yourself it provides entertainment. Different forms of entertainment can inspire you while you work. Or entertainment can help you relax by taking your mind off of work. This is what sports do for some people. Others instead might watch a movie or listen to music. Inspiration, motivation and relaxation are very useful in the workflow process.
I am not a sports guy or fan by any means but that is a very harsh judgment. Look at all the industries directly and indirectly connected to those sports teams, players and events and add to that all the news stations and news papers etc. and they all provide jobs and eventually pro-sports might even contribute to new medical treatments and therapies. And in the worst case, huge sports events like the superbowl or olympics usually bring tourism and infrastructure projects to wherever they are being held.
On top of that, "watching the game", especially in the stadium, actually does serve social and therapeutic means and needs - do not underestimate how much of an outlet it can be for some people.
By and large, any sort of entertainment is big, big, big business and in our IT world, what is facebook but entertainment? And most technology companies nowadays are mostly providing means to get access to some sort of entertainment.
On the same account, you could question art, music and fiction literature.
So, do not look down on "entertainment" because as they say, "all work and no play...."