Breaking the events of the past in an FPS would be coool.

If you don't get it, read the spoiler:

SPOILERThe actions done in the previous rounds are repeated so that the new round of players can (hopefully) change those previous actions or use them to their advantage. For example, there was no reason for the blue player to kick the tire in the third round, until the fourth round where the orange player used it as cover.

The "unlinked" symbol suggest that the previous action cannot be fulfilled, and thus the AI has to change it's actions and adapt. Player controls the first person manually, then the second, third, fourth, and fifth. The previous actions are repeated until something in that character's direct environment is changed, unlinking them from the past and making them an AI/player controlled player to adapt to the new changes.