As you guessed correctly , the two class comparison simply consists of a simple linear hypothesis test followed up a multiple hypothesis correction step.
In particular, for each feature/column of the selected dataset we are fitting a simple linear regression model to the chosen phenotype of interest. The estimated regression coefficient and its standard error then fed into the adaptive shrinkage method described in https://doi.org/10.1093/biostatistics/kxw041 to obtain moderated effect sizes (posterior mean estimates) and corresponding q-values (FDR). For the binary features, this methodology is being roughly equivalent (the only difference is the shrinkage step) to using a t-test with a pooled variance estimate.
Also, for the sake of reproducibility we keep the code used in this analysis in this github repo: https://github.com/broadinstitute/cdsr_models/blob/master/R/linear_association.R