How can I fill this gap between the plasterboard and window architrave?
I am having a bit of a problem understanding why plaster board or sheetrock would be finished to door and window jams without a casing/molding frame. In the few instances I have seen flush fitting walls to doors/windows, the wall covering is a thin, finished edge panel of some type, not 1/2" rock. In your case, the pic looks like the edge of the was was simply finished with some type of caulk or sealant to the jam, and either the jams have cupped or the caulking has shrunk over time causing the gaps to appear.

My first option would be to case the doors and windows with a molding. This would cover the gaps and secure the "flapping" wall board.  The second option could be to use an elastomer paintable caulk/sealant to fill the gaps. I might use some finish nails to tighten the wall board and counter sink the nails slightly and fill and finish the holes. Hint: cover the jams and edge of the wall board with blue painter's tape before applying the caulk. Smooth the caulk into the gaps with a putty knife, then immediately remove the tape, leaving a nice crisp, straight line.