Ref down. Thank heavens for commonsense in the midst of battle!

The referee, close to the action as the best place to monitor the tackle, gets a shove from Juan Smith of South Africa which sends him stumbling into a tangle with Jimmy Cowan and Schalk Burger who is tackling Cowan.

How does the match come to a stop in such a case?

The referee blows his whistle. In this case the referee was in no state to blow his whistle.
The assistant referee steps in, preferably by blowing a whistle as he is likely to have one. That seems not to have happened here.
The players stop playing, which is the commonsense thing to do. Even though this match was played with great intensity, commonsense could still rule and play stopped, the players clearly concerned for the referee.

First aid attended to the referee who was able to continue. Had he not been able to continue the Number 1 assistant referee would have taken over.

How do you restart?

Law 20.4 THE TEAM THROWING THE BALL INTO THE SCRUM
(d) Scrum after any other stoppage. After any other stoppage or irregularity not covered by Law, the team that was moving forward before the stoppage throws in the ball. If neither team was moving forward, the attacking team throws in the ball.

New Zealand were moving forward.