If you're not familiar with "Shiritori," it's a game where two people make a chain of words where the last letter of one word is the first letter of the next word. For example:
"caT" -> "TreE" -> "EgG" -> "Great" ...
(capitalization added for emphasis)
And so on. It's a familiar game in Japan so the game shouldn't need any introduction to your students. The twist for this game is that each player is looking for a word that will allow the words to become a cycle, so that the last letter of the last word is the first letter of the first word. To continue the example above:
cat -> tree -> egg -> great -> team -> magic -> (cat...)
The player who thought of the word "magic" is the winner because that word completes the circle. I make a rule for the students that they have to play at least 4 words before they can try to complete the circle. Otherwise it's easy for students to think of a pair of words that finish the game immediately (like "elephant" and "tree") and that's not very exciting!
I demonstrate the game by playing it with the JTE, writing the diagram from the worksheet up on the blackboard. When we finish I count up the number of words in the round, and circling the number and writing it up on the blackboard. There's no particular reason to do this, but it can be a fun thing to ask after the activity finishes if any pairs had any especially short or long games.
I pass one paper out to each pair of students and have them play with their partner. Each partner takes turns thinking of the next word. You can set different rules for the game like limiting words to come from the textbook or other sets of vocabulary that you want them to review. I find this is a good activity to play with first-year junior high school students as they often start searching the dictionary in the back of the textbook to find more words. This helps teach them alphabetical order, how to look words up in a dictionary, and introduces vocabulary that they'll be learning later in the school year.
I find this is a good activity for those times when you suddenly get asked to do a class and need a good general activity. Some groups will finish 4 rounds much faster than others so I wouldn't recommend on filling an entire class with it.