The thing with Lebron is that he's a professional athlete on a TEAM, and he is paid to play basketball. He knows that he needs to play in order to win games and championships. The NBA is a business, and the owners and players are all trying to make money. If Lebron were to take weeks off to recover between games, it would hurt the team's chances of winning, and it would also hurt his own chances of making money (if LeBron's team misses the playoffs because he's not playing, he'll lose out on a significant amount of money from playoff bonuses. He'll also lose out on endorsement opportunities, as sponsors are less likely to sign a deal with an athlete who isn't winning).
So, while it is true that it is not optimal for Lebron's body to play 82+ games in a year, he is still going to play because it is his job and it is what he loves to do. Plus, he's super competitive, and he wants to win as many championships as possible. He also knows that he can make more money by winning championships. So, while it might be better for his body if he took weeks off to recover between games, it's not in his best financial interest to do so.
It's not entirely fair to compare Cooper Teare, a newly signed pro runner whose not racing much in the early season with Lebron, who plays as many games as possible.