How was this play able to happen?
From MLB stats:
A stolen base occurs when a baserunner advances by taking a base to which he isn't entitled. This generally occurs when a pitcher is throwing a pitch, but it can also occur while the pitcher still has the ball or is attempting a pickoff, or as the catcher is throwing the ball back to the pitcher.
Note that steals happen (or are at least initiated) when the ball is not yet put in play by the batter.
In the video, Baez puts the ball in play and is therefore entitled to first base. It's poor defense (both execution and decisions), but it's just the batter becoming a runner and advancing safely to first base (and then advancing to second on the bad throw). No steal.