the coach has apologized profusely, so he must have done it intentionally.
That does Not however answer the question of what was the dolphins player doing that far out of bounds on a play like that.
Other players can, however, go out of bounds and return to the field of play to make a legal tackle on a ball carrier - so long as they have established themselves as being in bounds before making the tackle (at least two full steps in bounds). Why would a player deliberately run up the field out of bounds? Probably because it is illegal to tackle or block a player who is out of bounds so players who are covering a kickoff return can get upfield quickly without worrying about other players getting in the way. So long as they take at least two steps inbounds before making a tackle, they are good to go.
He was breaking the rules and committing what should have been a 15 yard penalty, that's what he was doing.
I believe this took place on a punt by the Dolphins, and the Dolphins player was probably lined up on the far outside in what is known as the "gunner" position on punt teams. His job is to run downfield as fast as he can and be the first one (along with his counterpart on the other side of the line) to get to the punt returner.
On plays like this, it's not unusual for the "gunner" to make a move to the outside to get around the player (sometimes two players) that the punt return team lines up on him to impede him . . . and get blocked out of bounds in the process.
That does Not however answer the question of what was the dolphins player doing that far out of bounds on a play like that.
<><><><><>
Watch the play from the beginning, on this or any punt. The guys out wide routinely are pushed out of bounds by the return team.