I have received a clarification on this from Marc Okrand, and his answer
even brought a new word:

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What I was driving at is that a {qa'rI'} at or from which one can enter
or exit is a {DIn}. There may or may not be a (closed or open) door or
gate there, but if there is, that door or gate is a {lojmIt}. That is,
there's no special word just because it's a {qa'rI'} door.

(By the way, a doorframe or something similar — something constructed to
hold a door or gate, whether the door/gate is there or not — is a
{lIvqa'nan}.)