TOTM is "Theater of the Mind" for the puzzled.
Using my Surrounded houserule, it would work the same.
Surrounded: When you end your turn with enemies on opposite sides of you, you become Flanked until the end of your next turn or you there are no longer enemies on opposite sides of you. When Flanked all attacks on you have advantage.
Adjudicating this in TOTM should be about as easy as on a grid. Can they reach the opposite side? If so, they are threatening a flank. Then on the creature's turn they can get of the threat (killing/pushing a creature threatening the flank, taking OAs by moving, etc) or not.
In TOTM, threatening a flank usually happens on purpose. Preventing it requires a defensive line that is anchored at each end; if the line isn't long enough for anchors, the ends are vulnerable to being flanked. So rolling up the line becomes a threat.