When Master Yi tempered attacks with 7 might to a Darius with 5 might, Draven player who has Darius reveal hidden card Switcheroo. Does the Master Yi which is at 7 might gain the might of Darius being at 5 or at 7 because he played the second card this turn?

Master Yi gains 5 — Switcheroo swaps using each unit's current Might when it resolves, and Darius is sitting at 5.

Darius's "+2 Might when you play your second card" is a triggered ability that only goes on the Chain after the card that made it your second card fully resolves (FAQ #5184). Since Switcheroo is played before any such trigger fires, the swap uses Darius's current 5: Master Yi drops to 5, Darius rises to 7.

Then, if Switcheroo was indeed your second card this turn, Darius's trigger resolves afterward: he gets +2 to 9 and readies. Either way, Master Yi keeps 5 for the rest of the turn (FAQ #7874).