Most of baseball takes place in a single one on one interaction: Pitcher throws, Batter hits. In that sense, it is fairly easy to tease out the performance of the batter and the pitcher based on the result in many cases. A home run, a walk, a strike out, all of these are entirely based on the one on one matchup and the other eight players might as well be having lunch.
Where baseball statistics become complicated is when the defense comes into play. Defensive statistics in baseball are indeed the weakest area of statistical analysis in baseball, to some extent because they're somewhat subjective, and somewhat because they do impact other players.
But even then, mostly defensive actions in baseball are still a singular player's action. A defender has balls hit towards him, he can field them or not field them, and you can measure how far away he ranges, what percent of balls he successfully fields, etc. The quality of the hitter doesn't really matter to the defensive player's performance - a hit to a particular spot is a hit to a particular spot, more or less.
And for the hitter, it's indeed complicated to take the defensive performance (and the park element) out of his performance, but once you work out how to measure defensive performance, it's not necessarily that hard.
Compare this to football. A running back rushing the ball depends on five or more offensive linemen, as well as the defensive players on the other team. To work out how good a four yard rush was, you have to factor all of that in, plus the game situation - 1st and 10 vs 3rd and 5, a 4 yard rush is very different.
Basketball and Hockey have similar problems; the other players on the court/ice make a big difference to your performance, so you need to figure out how to factor them out. The more variables you have, the more complicated it is to work out the statistics. 10 or 12 players on the court/ice means that many variables - far more than you really have in any baseball interaction (2 or 3 variables, typically).
Baseball also has a lot of individual interactions to track, meaning you can get a lot more meaning out of them. 600 plate appearances per year for batters; 150-200 innings for starting pitchers (meaning 600-800 batters faced or more). Those numbers mean you can get a lot of information out of even complex interactions.
On the other hand, you have football, where running backs touch the ball maybe 300 times a season, quarterbacks maybe a bit more than that, and the rest of the players nearly all have fewer than 100 touches a season. Basketball has a bit more in the numbers department (thousands of shots per season), and that's why it is more-or-less the second best statistical sport. Hockey you have a few hundred shots per season, perhaps, and there are some things you can do based on game appearances - which is where the best stats are found in hockey (like the Fenwick or Corsi statistics). Quantity will somewhat make up for quality in statistics; Baseball, though, has both.
Finally, while baseball is definitely easier to track statistics on, it's also the first sport where it was tried. Baseball stats (box scores) have been around for a century, with fairly detailed statistics for much of that. The sabremetric movement began in baseball in the 1970s, and thus it's more advanced than it is in other sports regardless of difficulty. It's possible it stared in baseball because of the simplicity, but it's also possible it simply was first because baseball was the most popular sport for decades and thus had the most detailed statistics.
