Translation:A cabinet is a piece of furniture, like a big box with a door or doors.
You can think of this as a condensed version of "Ŝranko estas [tia] meblo, kvazaŭ [ĝi estus] granda kesto kun pordo aŭ pordoj" (A cabinet is [that kind of] furniture, as if [it were] a big chest with a door or doors). As a conjunction, kvazaŭ is, indeed, roughly equivalent to "as if" in English. But, when I was still learning how to use it, I always found it helpful to know that it's also used as a prefix, which is nearly identical to quasi-.
"As if" and "like" mean the same thing, it's just that sometimes you can only use "as if" if you're trying to sound poetic.
"I felt a great disturbance in the Force, as if millions of voices suddenly cried out in terror and were suddenly silenced."
Even though that sentence is a bit different from this one, I think it illustrates the similarity in meaning.
The help text here for ŝranko doesn't mention wardrobe, but in other places it does.
I would not think of a big box with a door as a cupboard, a cupboard should have shelves to hold cups and other kitchen stuff.
Then there's built-in cabinets and cupboards, so they aren't exactly like a box.
It's fun sometimes to think of or use a thesaurus to find related words like closet, wardrobe, cupboard, cabinet, etc. and see how translations are similar or differ.