Mike is seen playing piano on the "Mike, Come Back to LA" footage. He can also play basic guitar. I imagine he is more than capable of writing bare boned chord progressions for his song ideas. As mentioned on the older thread he most likely sang/hummed melody ideas to someone who transcribed them.
Don't remember where I read it but that's the way Mike described his writing of a specific song. he hummed or sang his idea to Carl who wrote the music down for Mike
In the Goin' Platinum TV special, Mike described writing "Goin' To The Beach"...I can't remember how he said he conveyed it to Carl, but it probably was singing or humming, and then he said Carl did a demo on the guitar.