The reading is the same as 引く, which is "to pull." When you play a stringed instrument, you are pulling the string in a direction to make it vibrate and create a sound. So, "to pull" and "to play a stringed instrument" share a reading. It's a bit more of a stretch for instruments with keyboards, but pianos do at least have strings...
Mika said that she feels relaxed when she plays the ukulele.
When I tried to play an old guitar, one of the strings broke.
I was thrilled by the news that he started playing piano again.