There's two main ways of sliding up a note on the bagpipes.
[Disclaimer: I play Flemish bagpipes rather than Great Highland Bagpipes, but I see no reason the same techniques shouldn't apply to both variants of the instrument.]
The video doesn't show the player's fingers at the vital moment, but I would suspect that he does it by smoothly rolling the finger off of the tone hole, opening more and more of the hole so that the pitch slides upwards in a controlled manner. Flute and low whistle players often use the same effect.
The other option is to increase the pressure on the bag, which forces more air through the reeds and therefore bends the note upwards that way. Bagpipe pitch is quite variable and you spend a good deal of time learning to control the pitch by applying constant bag pressure; this technique reverses that training and uses that variability as a musical effect.
However as I say I personally suspect that it is the finger-roll that is being used here.