The eyes themselves are reminiscent of a pride demon - on the mural, at any rate - but I think the description means they are something else. A "shifting, shadowing mass" sounds less like a static creature like a pride demon and more like this:

And of course the blazing eyes part, and the implication that it may be more than one creature. I don't think Solas is much like a pride demon except for him having an issue with pride. What does Cole say, exactly?
Cole said these 2 things in Trespasser that got us theorizing.
"He did not want a body. But she asked him to come. He left a scar when he burned her off his face."
If Solas was a spirit of Wisdom, Mythal gave him fleshy form and marked him. He removed it (as we all know he can) and scarred himself (the scar on his forehead).
Then Cole says:
"Bare-faced but free, frolicking fighting, fierce. He wants to give wisdom, not orders."
Solas said he was Solas before Fen'Harel and if he was a spirit made real and possibly corrupted (wolf demon form), he would have become Pride and forced to do what was against his nature, but manifested into a human-form like Cole, he would not become a complete demon.
So that got things going and we started remembering how Solas knew that Cole was a spirit made human, how he didn't want another spirit lost. How his friends were also spirits and the dying Wisdom could have been related to him. His fear of binding someone like Cole wanted, and his loyalty to Mythal could also be because she bound him to her. Things like that. It's been fun to discuss!