The threefold (GDS) model was developed in rgfa in 1997, and is not to be confused with the more recent GNS model and Big model. A good source is the website of John H. Kim.
According to Kim's website the threefold model classifies decision making processes (contrary to GNS/Big model, where creative agenda classifies the psychological reward the group gets from playing). In particular, the threefold gamism, according to Kim's site, is defined as follows:
Gamism is the style which values setting up a fair challenge for the players (as opposed to the PCs). The challenges may be tactical combat, intellectual mysteries, politics, or anything else. The players will try to solve the problems they are presented with, and in turn the GM will make these challenges solvable if they act intelligently within the contract.
I recall that Brian Gleichman, a participant in the rgfa discussions, has some criticism of threefold gamism as presented by Kim. What is the criticism?
I think this is an interesting question to ask, because GDS had a reputation of being dismissive towards its gamism (much as GNS has a similar reputation about its sim). Gleichman was, as far as I remember, one defending or giving positive interpretation of GDS gamism.