It could.

It could also mean the president played a round of golf and scored 78, or that there is a candidate named Round which is being put forh as the likely winner in 78, or...
Headlines are notoriously vague and ambiguous. They have so little room to work with, and the results are sometimes disastrous.
Honestly, without at least a little information from the body of the article, I would have no idea what it actually meant.
They also do not conform to normal rules of English, so what we would say as "Presidential Round" might get shortened to "President Round" for space considerations.