Core KTV vocab. 点 here means 'to choose / order' (same 点 as 点菜 'to order food'). Related: 切歌 (to skip a song), 排麦 (to queue to sing), 抢麦 (to grab the mic).
culture
Also used for radio/livestream song dedications: 点一首《...》送给我女朋友 — 'I'd like to dedicate ... to my girlfriend.'