Hey,
playing many casual games simultaneously is a challenge to remind "what strategy was I using in this and that game"... and, besides, the in-game strategy shown in the unit tab is the the one that was picked in the lobby. In a casual game the only way to know the actual strategy that is being used is to have a look at the stats of the units (and their costs).
Suggestion: to add "strategy" to the game summary when hovering the game from the casual game lobby... something like this:
Would be very useful, the same way that the clock was added some months ago.
Cheers.