At 53 years old and assuming the same distance covered, it's uncertain that Jurgen Klinsmann would be able to individually match the 110.7km covered by Arsenal players during an average 90 minute game.
In doing so, his speed of 73.8 km/h would eclipse the record of 44.72 km/h (27.8 mph), seen during the final 100 meters sprint of the World Championships in Berlin on 16 August 2009 by Usain Bolt. (Bolt's average speed over the course of this race was 37.58 km/h or 23.35 mph.)
The sending off in the 12th minute further compounds the problem for Herr Klinsmann with him having to speed up by a multiple of 5.
His increased speed of 369 km/h would be 1 kph faster than the 368km/h recorded on trial runs of Germany's ICE 3 (Inter City Express) trains.
With all this considered, one is sadly forced to conclude that the anecdote mentioned by the OP is somewhat lacking in veracity.