On word counts does a hypenation of two words count as one?

This is what Microsoft Word does the counting.  (Amusingly enough, this is also what I learned 55 years ago in high school.)

Jayson asked if there was a way to make sure that Word ignored hyphens used in compound words when doing word counts. For instance, he wants Word to count "real-time video" as three words, rather than two. There is no native way to do this in Word. The reason is quite simple—the generally accepted rule is that a compound word is always treated as a single word. For instance, the compound adjective "real-time" is a different word than "real time."

There are three kinds of compound words—the closed form ("firefly"), hyphenated form ("daughter-in-law"), and open form ("post office"). Compound words are often hyphenated to remove ambiguity (i.e., an "old-furniture salesman" clearly deals in old furniture, but an "old furniture salesman" could be an old man. In most contexts you wouldn't have the same problem understanding "used furniture salesman").

Using the example "real-time video," the word count for that phrase should equal two, since "real-time" becomes one word by virtue of the hyphenation. In the sentence, "Talk to your father-in-law," the count should be four words, since "father-in-law" is treated as one word. Counting "father-in-law" as three words would be blatantly incorrect, since you're referring to one person. So, once compound words are closed or hyphenated they are counted as one word. If the compound word is open, e.g., "post office," it is counted as two words.

https://wordribbon.tips.net/T009228_Ignoring_Hyphens_in_Word_Counts.html