To be fair to Rosberg, it was his life goal to win the championship. He did it and retired to enjoy life with his family. You can't fault the guy for that. That was his goal.
Hamilton's goal is to set records. They're totally different mindsets.
You've got it totally wrong. Hamilton's goal is simply to be the best driver he can, to perfect his skills as much as possible and continually test himself against the best drivers. The records that come with his success are merely a way of measuring it, not a goal in themselves.
Take championships. When he won his third, he was more concerned with having equaled the achievement of his hero, Senna, than he was with the number three per se. When he won his fourth, it was more about becoming the most successful British driver than the number four. It's not about the raw numbers, it's about achievement and measuring himself against the greats.
If anything, Rosberg was more interested in records than Hamilton. He just wanted to get a championship to "put a tick in the box", then he quit. He wasn't interested in continuing beyond that as he had no real love for racing, he just wanted that tick. He was also willing to do anything to get it, often employing underhand tactics against Hamilton and ultimately needing poor reliability for Lewis to achieve it.
Rosberg was undoubtedly quick on his day but was a totally forgettable driver. Many people have already forgotten about him this year - ask the average person with a passing interest in F1 who the current world champion is and they'd probably pause for a second or two. He'll go down in the history of F1 as a forgettable driver who lucked into a single championship.