If they were actually given two minutes, there wouldn’t be any difference to the wake turbulence separation since the previous departure would have started rolling from the same holding point. Three minutes would be correct for an intersection departure.
Unless, of course, a minute had already elapsed.
I think this is more likely to be some sort of separation requirement, either imposed by a next sector to reduce overload, or by a procedure.
We don't have the full facts but, on the basis of the limited information given, wake turbulence provides one perfectly reasonable rationale for the backtrack:
Two minutes separation required due to same track (the OP said as much; it is not for wake turbulence it is just the ICAO departure separation if No1 is 40kts faster)
But for the intersection departure 3 minutes wake turbulence separation might apply subject to aircraft cat (not specified in this case)
By chosing full length instead, the No2 could save up to 1 minute by reducing required separation to 2 minutes again