I think he is trying to say that he didn't spend a lot of time on it. It's not a word that I've ever heard, but I'm assuming the author thought it would be a good word to use because a "glance" is a quick look. So, he's trying to say that he paid attention to it ("not dismissively"), but he didn't give a whole lot of extra time and attention to it.

I understood it more clearly and got a new phrase "two cents worth." Thank you so much!

I agree with Sarah's answer; a glance is a quick look, or, used as a verb, "to take a quick look". It also means a hint or flash of light, in the literary sense. The writer is using the word metaphorically to describe and also compare the way he's listened to the recording, i.e briefly, with faint (not deep) interest... That's just my "two cents worth". :)