First, let's expand the contraction to clearly show the subject and the verb:
That is two words.
"That"--demonstrative pronoun (singular) [https://en.wikipedia.org/wiki/That ]
"is"--a linking verb (singular; NOT an action verb).
When a linking verb is used
"A linking verb ("is," "are," "was," "were," "seem" and others) agrees with its subject, not its complement."
[ https://writing.wisc.edu/handbook/grammarpunct/subjectverb/ ]
"words"--subject complement (quantified by "two"--numeral determiner)
"A subject complement follows a linking verb; it is normally an adjective or a noun that renames or defines in some way the subject."
Based on that, I don't think it would've mattered if there were 1000 words, as long as "that" referred to something singular, such as an essay...or, another example, a Stephen King novel: I read Duma Key. That's 609 pages!
The last page is two sentences:
Know when you're finished, and when you are, put your pencil or your paintbrush down. All the rest is only life.
(Which reminds me, something singular, as I put it, may be a mass noun, not necessarily a countable noun, if I'm not mistaken...but I'm finished now.)