Onomatopoeias:
ピューン -> sound of a beam (as in a beam gun), "pew"
パンパン -> either "smack smack" or "bang bang"
ドーン -> strong hit, "blam", "boom" or "clonk"
ピコピコ -> this weird sound may by cartoon game characters when walking, mainly in 8-bit games or cartoonish games
My best guess is that they are playing a Super Smash Bros. clone, with the first one being a beam move, the second normal attacks, the third a heavy hit and the fourth a particularly cartoonish character running (Kirby?).