Piccolo is strong enough to make Vegeta need to put effort in. Not worth the hassle. He just wants to bully a bereaved 6 year old. I can steal candy from a baby and beat a pigeon in a fight, but if a pigeon wants the candy it can have it.
Vegeta got beat up by Freeza using like 3% of his power, right?
Nah, Piccolo shouldn't be able to do that at all. Vegeta was the only one who could see final form Freeza's movements and avoid them, while Piccolo could do nothing. In the anime, Piccolo was trembling and flabbergasted when Vegeta powered up, referring to both him and Freeza as monsters. Vegeta was far beyond Piccolo's abilities for it to even be needed any kind of effort other than easily beating Piccolo up.
My guess is that Vegeta didn't want to conquer the Universe and reign supreme as he was saying. I think he saw Gohan being in denial about his father's death and intentionally provoked Gohan by saying he was the ruler now so Gohan would be mentally tough and not be shaken, in denial that his father died. When Gohan beats Vegeta up firstly, Vegeta says "huh I was going easy on you because you're a kid but you had to raise it to that point"... Then Vegeta flew upwards and Gohan also did, to which Vegeta said "Are you sure you're ready for this?"... Seems like he was kinda hesitant, didn't want to beat Gohan up but just make Gohan tough mentally by accepting his father was death. When Bulma tried to stop Vegeta from tasing Gohan and tried to break down their fight, Piccolo made a signal for her not to interfere and let them have it... And while Vegeta was repeatedly punching Gohan in the face once he got serious, Piccolo was just watching with a serious expression and not worried. Seems to me he knew Vegeta had no killing intentions. But then it seems Vegeta lost it a little and was aiming to finish Gohan (perhaps because he saw Gohan would not accept his father's death and would be better off dying as well) then Piccolo said for him to stop, with the scene cutting to Gohan crying saying his father will come back, that he's sure of it... Seems like Piccolo wanted, in a subtle way, for Vegeta to pay attention to Gohan saying that all injured, showing Gohan had a deep belief and not just denial. Then Vegeta was like "huh your optimism makes me sick" and left. He just imo tried to make Gohan deal with that and Piccolo saw through that and understanding Vegeta, said for him to stop knowing Vegeta would realize it wouldn't be better killing Gohan... I also feel Vegeta may have been feeling sad about Goku dying and his way to cope with that was making Gohan to not be shaken emotionally and be tough mentally, then perhaps he saw through Gohan's genuine optimism that it may not be simply denial, but there may be a possibility of Goku coming back.
Btw that filler is inconsistent within the same anime continuity as in the next episode Vegeta was already back in the same spot he was before teasing Gohan and gave them advice on how to solve the issue of Goku reviving on Namek which didn't exist anymore, while in this chapter he laughed at this predicament. So idk why the anime made a total contradictory filler knowing Vegeta would give them this advice. At least if the anime featured Vegeta flying back to the local and giving them the advice --- but then he would know that was a possibility and would purposely hide it, which with my take on the scene above would only make sense if Vegeta thought on his way flying off of a possibility to bring Goku back and came back saying "you idiots, use your brain for a while, I just needed a few seconds to figure a way out...!!" ...
