I love to emphasize. Here I'm emphasizing "determination." Is it the right way to do it?
"If one word can sum up his career, it is determination—determination to fight back and do the impossible."
What you're doing here is anadiplosis, "repetition of a prominent and usually the last word in one phrase or clause at the beginning of the next" (MW). And yes, it's long been recognised as a specific rhetorical device which adds emphasis to the repeated word (see Wikipedia, among other sources).
However, what makes it anadiplosis isn't the em dash; it's the repetition itself. Whether you use an em dash or an en dash is a whole other question, discussed here (in summary, American usage favours an em dash, British usage favours an en dash). A semicolon or full colon would also be possible in this case. There's no single "right" choice between these options - it would come down to the rhythm of the paragraph, and/or to personal style.