Does Bone Skewer trigger Kennen's legend ability, since it makes the opponent play the revealed card?

No. Bone Skewer makes the affected player play the card themselves, from their own hand — it is not played by you, even though you caused it to happen. Kennen's legend ability requires that you are the one playing the card, so it does not trigger here. It would only work if you were the one playing the card yourself and had control and ownership of it, such as with a future card that lets you play a card from someone else's hand under your own control.