Just played with it some myself... looks like when you shift the cursor to create a new line, the drawing process starts the new line at the edge of the terminated line, but then ends it at the grid point it is snapped to. It always starts and ends exactly even with the grid, so the tool is doing what is intended... the issue is that the rendered line that comes up around the points in the vector drawing isn't compensating for the square of the grid that isn't actually overlapped by the render. In the drawing above, the top-left square out of the 9 squares interacting with the art.
I think most vector art programs compensate for this by having the lines all bind together into a single vector object when a drawn point lands on the starting point, forcing it to re-render the whole thing, and eliminating any holes or awkward angles in the process. Essentially, you're drawing lines until they come together, at which point you've drawn a polygonal object, at least for the sake of the rendering engine. In the way the tool is working here right now, you've just been drawing lines.