Skills gained from "playing" with your pet are minimal comapred to skill gained from taming.
This buff definetly increases skills gained from taming (tested TT value gained and difference was clearly visible). So this i can confirm.
In theory it should also increase the skills gained from "playing" with pet too - since many skills are actually exactly the same skills you gain while taming but there are two issues:
1) since the skillgains are much much smaller from doing this - it would require much more time to measure it
2) it is probably NOT worth the cost of running the buff in this situation.
Falagor