A little question :)

It's just about politeness for a lot of people, man.... After all, we're getting free games if we win.

What is true is that some private giveaways have rules were you DO have to thank to be eligible. If you don't, the creator can ask for a re-roll on the winner. These rules HAVE to be explicitly mentioned, though...

And yeah, randomly generated.

The winner is randomly selected, yes. People usually thank the giveaway creator because, well, they are thankful. It's a question of manners.
Edit: 9 seconds too late. :P

Yes, winners are chosen randomly.

People (generally) say thanks on giveaways out of politeness, but to me, it makes little difference, I'd much rather have the winner say thanks personally over every entrant saying a mindless thanks comment on the giveaway.

random selection, thanking is politeness, some ga creators don't care others do

For me a "thank you" for the recipient of a giveaway is one steam card (whether or not it is from the game recieved). Thanking ahead of time is out of politeness- "thank you for posting this" etc.

My problem with giving thanks: I used to thank everyone when I first joined the site. Then I noticed a lot of thanking that was simply random text copy paste. Too many people use scripts to thank people. I at one point created a giveaway where I asked people not to thank me, but rather comment on my profile picture (which was different at the time), and I still got the majority of comments being some variation on thanks (excluding the witty ones, like other languages and then asking if that counted, which means they obviously read). It's annoying to see fake gratitude. If I could trust thanks were legitimate, then I would like it, but seeing copy paste (especially if you run multiple giveaways at the same time and see the same comments) actually makes me mad; don't just pretend to be grateful when your bot enters giveaways or comments for you.