Right, so the title is a mouthful and this patch is a partial bug report in some ways, but the gist of the situation is this:

At the moment, increment snapping only produces the right transforms when it is used with axis constraints and/or the viewport is aligned to an axis. If you try to use increment snapping without axis constraints, with the viewport rotated to an off-axis perspective, as in the video above, you won't get desirable results; the snap increment seems be influenced by the view matrix. This means that increment snapping works 90% of the time, but it breaks quite thoroughly for that other 10%.

Near as I can tell, this behavior was introduced in 4eda60c2d82d, and it looks the culprit here is the matrix math that's done immediately before and after calling transform_snap_increment() in applyTranslation(). Removing that math appears to fix the issue (that's all this patch does), but I don't entirely understand why. I've tested the edge-cases that have come to mind, but I don't know what I don't know on that front.