Delay turn isn't skip turn, it simply places your character at the end of this turn for his actions instead of the designated time.
And indeed as stated before, this can definitely mean your character goes twice in a row, a very powerful combo in several situations.
I also have not played many of the mentioned games or tabletops, but did dable in some D&D. And I don't know how the OP played it, but for me it was always "heroes act", "opponents act". Sure, we could choose amongst ourselves which of us went first, second etc. but like X-Com it's not the same as here where a turn isn't one side's actions, and the next turn another, but one turn rules everyone.
