My favorite is the "Gaze of Death". Everyone stands in a circle, looks down, then on a cue everyone looks at one other person's face. If any people make eye contact they both must act out horrible deaths, and they fall out of the circle. The game continues until everyone dies or one person is left standing.
I would approach one of these groups of people and introduce myself.
Then I would go to the next group, introduce myself and then ask if they have met ... (pick someone from the 1st group).
The few attempts I've made at games during gatherings didn't work because of poor participation. Maybe I need to be more assertive, with "we're going to do this" instead of "who wants to do this."
"Everybody round up, it's time for an activity so that we can all get to know each other a little better. TRUST ME! It's going to be fun."
text everyone a word which connects you two. Then, you print a list with all the names, and distribute it. Everyone must find out the word connecting you with each one. But: the people can only reply "yes" or "no" to the questions.