“Poor Summers, he should have gotten a songwriting credit.”
For playing some arpeggiated chords the whole song? I’m sorry, but it’s probably his least creative guitar riff, and he’s normally a pretty creative guitar player.
But you can’t copyright riffs, or chords, or arpeggiated chords. You can only copyright melodies and lyrics, and that’s why Sting got the credit and not Summers. He should have made an agreement like some bands where all members get credit on every song, no matter their individual contributions, but he didn’t, maybe because Sting might have walked if they had demanded it.
Listen to the demo. The song that Sting wrote was the most boring song, that wasn’t interesting at all. Without what Summers added, it never would have been a success.