Isn’t “Eye-glazing” a popular word? Why isn’t it included in major English dictionaries?

"Eye-glazing" isn't that common at all. "Eye glazing over" is certainly used, as in "his eyes glazed over". In your main example, the person is commenting on "one of the least-interesting paragraphs" you have ever read, and he is saying, "ok, after these very boring paragraphs, it gets less boring(eye-glazing)".
The term "eye glazing" is usually used in the sense that the person is so bored that his eye glazes over. Also, the "The Burglar on the Prowl" example has the same meaning of boredom.

But is this common? Is "eye glazing" common usage? Taking a look at an Ngram:

By far, "glaze over" is used the most, whereas "eye glazing" although it is used, is not that common. Perhaps that's why it isn't included in most dictionaries.

I usually hear this as his eyes glazed over or glazed-over eyes; the phrase glaze over seems well documented: glaze over on Dictionary.com. Your derived adjective eye-glazing sounds less common to my canine ears, though still perfectly clear.

I don't think ‘eye glazing’ is as common a term as eye-opening, which has almost become a single word.

There is a journalistic term mego (from - My Eyes Glaze Over) used to describe a passage of long winded poetic description dropped into a scene.

"Eye-glazing" means "so boring/tiresome that it makes you sleepy". Remember that Tom & Jerry episode where Tom has to tape his eyelids to pretend he is standing guard? He was dead tired but wanted/had to stay awake (like you do, too, in order to finish the article) so he tried to force his eyes open. What happened then? His eyes glazed!