Yes, I believe the physical 'thank you' note from the developers included in The Witcher 3 pc game will indeed increase sales. The target audience that purchases this game may not be familiar with such a touch of old-fashioned gratitude but they will respond by keeping the note and passing the word along to their friends. That little act of thoughtfulness by the game makers will be just enough to set The Witcher 3 apart and push the sales higher.
Who would care? We should be thanking them for developing the game. I think that it's nice and all, since we spent the money that goes towards their pay cheque. It is a nice gesture though, but you wouldn't by anything just because it says 'thank you'. It's like buying a type of cereal you don't like just because it says 'thanks'.
I think a thank you note will just make a few people happy. Those who bought the game were going to buy it regardless of the note inside. Those who were not going to buy it are not going to run out and get it just because of a thank you note.
No, including a physical 'thank you'note with purchases will not likely increase sales. In order for a thank you note to have meaning and make an impression on customers, it should be handwritten and personalized to the individual. Otherwise, it will easily be seen for what it is: a marketing strategy.
I do not think that gamers are going to be interested in a thank you note. People who purchase the game are going to be interested in the quality of the gaming experience. If the thank you note contained a coupon or some sort of rebate for other games or use inside the game, it'd be a different story.