I would say that Troi is a strong player using her logical thinking and intuition but who was also extremely lucky.
She surprised Data with her 8 moves long winning sequence but then it instantly detected checkmate in 7 moves.
Data probably was taking into account known gambits and documented game plays but couldn't use them to determine looming defeat as Troy created a new / undocumented position. That strongly suggests that 7 moves deep search was used, which would simulate or possible follow-ups and leave no further surprises.
That means that Troi pulled out shortest winning sequence outside Data's search scope. If she had equally unexpected, brilliant move but leading to the victory even a tiny bit faster, Data would be aware of it thanks to 7 moves deep search.
That was light technical analysis but as Wikipedia states:
No complete solution for chess in either of the two senses is known, nor is it expected that chess will be solved in the near future.
The message here was that some problems aren't suitable for computers even if they have outstanding computing power. Intuition makes us superior to machines as it allows to simplify complex analytic problems.
Note that in 2D chess usually
- every other pawn can make 1 move
- knights, bishops, rooks and the king can make ~4 moves
- queen can make ~8 moves
So in the middle of the game there are usually around 20 possible moves. That means that if X move deep search would take 10 seconds, X+1 move deep search would take ~66 hours (60s * 20 * 20 as there are two sides in the game). In 3D chess there are probably many more pieces and many more moves, so X+1 move deep search could take days or even weeks.