Keeping as much of your style as possible, the simple way to avoid repetition is to pull the repetitive phrases inside your loop.
Now I'm assuming that what prevented you from doing this was the fact that Ruby's 'until' loop evaluates the exit condition at the top of the loop, which will therefore throw an error unless you've initialised 'word'.
This inconvenience can be avoided by moving from an 'until' loop to an infinite loop with an internal test / decision / exit condition, like so:
puts "Blurt out a word"
word_list = 
if word == ""
Now 'word' is defined before the exit condition is evaluated. And as a useful aside, a blank entry is not inserted into 'word_list'.
There are of course many other ways of doing this -- Ruby allows for cleverness over clarity. The above simply refactors your code and removes the repetition.