Surely the restart must be a dropped ball, due to the interference with play by an outside agent, yes? The substitute would be considered an outside agent. If a substitute enters the field of play without permission, the referee must stop play (although not immediately, if the outside agent doesn't interfere with play), but in this case, the play WAS interfered with by the outside agent. At that moment, the referee should stop play. The outside agent is removed from the field of play and its immediate surroundings (and either cautioned or sent off, if a player or substitute), and then restart play with a dropped ball. The restart should take place in the position where the ball was when the match was stopped. Since it was stopped in the goal area, the referee drops the ball on the goal area line parallel to the goal at the point nearest to where the ball was when play was stopped. At least, that's how I see it specified in FIFA law...
EDIT: Whoops! I had it wrong. The referee gets it right in the video with the restart being an IDFK! If the person who interferes with play is a substitute, then here's what FIFA says:
FIFA Guidance on a substitute entering the field of play without permission
Substitute or substituted player
If a substitute or a substituted player enters the field of play without permission:
• the referee must stop play (although not immediately if the player in question does not interfere with play or if the advantage can be applied)
• the referee must caution him for unsporting behaviour
• the player must leave the field of play
If the referee stops play, it must be restarted with an indirect free kick
for the opposing team from the position of the ball when play was
stopped (see Law 13 – Position of Free Kick).
I was thinking it was more like the infamous Sunderland/Liverpool beach ball incident a few years back. That was an outside agent, and the restart should have been a dropped ball... My bad, folks.