I'm comparing knockdown ChIP (3 replicates in the green) versus control ChIP (3 replicates in the orange), but the Fold (in the grey) is much lower than I expected it to be. I know the Fold isn't just Log2FC. Could the low Fold value be caused by shrinkage adjustments due to inconsistencies between the replicates?

The fold changes in the DiffBind report are indeed those calculated by DESeq2 after calling DESeq2::lfcShrink(). The help page for DESeq2::lfcShrink includes a number of citations for papers that describe these calculations in more detail.