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As a transcriber, I have seen many ways dots are used in literature —mostly to avoid redundancy. But I have seen dots unspaced from single letters, such as in the phrase "Guess the city: N.. Y..." The answer, of course, is New York, so the number of dots replaces the number of missing letters. Are these ellipsis points? To call them "ellipsis" would be wrong, but is there a literary convention that would allow me to refer to these omissions as "ellipsis?"

I could find no reference that offered a name when periods are used to indicate missing letters, or that periods should be used to indicate missing letters.

You are correct in thinking that this use of periods is not an ellipsis.

According to wiki - ellipsis:

indicates an intentional omission of a word, sentence, or whole section from a text without altering its original meaning

The only way I can think to describe the use of periods in "N.. Y..." is to say that the periods represent missing letters.

I did find that multiple em dashes are a convention used to indicate missing letters.

According to "The Punctuation Guide"

Multiple em dashes

Two em dashes can be used to indicate missing portions of a word, whether unknown or intentionally omitted.

Mr. J—— testified that the defendant yelled, “Die, a——,” before pulling the trigger.

From the faded and water-damaged note, we made out only this: “Was ne——y going to m—— K——, but now ——t.”

When an entire word is missing, either two or three em dashes can be used. Whichever length you choose, use it consistently throughout your document. Surrounding punctuation should be placed as usual.

The juvenile defendant, ———, was arraigned yesterday.

In many command-lines the period is a wildcard, which is a period or dot that denotes a single character. (It's a kind of regular expression, or a standard to represent a pattern for matching text.)

I have not seen the usage extend to punctuation generally, perhaps because the period is not a standard way to indicate blanks. Other punctuations are used for similar purposes: an apostrophe denotes the omission of one or more letters in a contraction, asterisks or dashes are common ways to denote missing letters, and I've seen question marks or underscores co-opted for similar use. I'd colloquially describe such a symbol as a letter blank.