The one reading I could give to this is:
Qatar used (uses?) to fly to/from LGW. This means that they need some sort of arrangements there: line maintenance (in-house or contracted), handling, catering, hotels, perhaps a station manager and a couple of duty managers... all while doing the same over at Heathrow. Maybe it makes sense for BA to cover that flight and for QR to concentrate on Heathrow, a bit like it was done with Iberia where IB took care of the first rotations out of MAD and BA the same with LHR, thus eliminating the need for night stoppers.

While can't be said that QR cares that much about costs (one of the many reasons I don't like that airline) maybe the winds are changing, the Emir might be growing tired of having to write a cheque ever year and this is the sort of avoidable expense that benefits everyone.