This is a spoof of a Japan-only game where you use the touch pen to massage and wipe down a variety of manga-style man-boys. No joke.
The game in question is Duel Love, a unique otome title where the heroine gets involved with martial arts tournaments at her school and, yes, towels off the bishounen participants.
By the way, Duel Love wasn’t the only romance game on the DS that used the touchscreen. A more famous example of that is Konami’s Love Plus, which was aimed at a male audience.
Original comic: P.S.すりーさん No.62