Like the absence of a dog's barking in the night, sometimes the biggest clue is what's not present. Holmes and Watson never mention the name of the game being played, and they never refer to certain other elements, such as the locations of bonus squares, when describing the placement of words on the board. That's because, while the visitor was scoring by the rules of Scrabble, the victim was scoring by the rules of Words with Friends. (This is alluded to when the captain says, "Our victim must have been expecting a friendly game, but unfortunately for him, his visitor had nothing of the sort in mind.")
Three factors contribute to differences in scoring: tile values, placement of bonus squares, and different bingo bonuses. As a result, the two players disagreed on the score of every move, but this disagreement did not come to a head until the final move, which created a word that is valid in Words with Friends but invalid in Scrabble (the disputed word was FI).
Here are the reconstructed moves:
|XY||Visitor||Scrabble Score||WWF Score||Diff||XY||Victim||Scrabble Score||WWF Score||Diff|
The visitor consistently scored higher in Scrabble than Words with Friends, while the victim consistently scored higher in Words with Friends. The differences in those scores, taken as indices into the alphabet, read FOURTH GEN KIA SUV, cluing the answer SPORTAGE.
Here's an image of the final board as seen by Holmes and Watson, including the final disputed play: