It's doing what you ask: the cutting machine follows a line, same as a plotter; from point A to B to C... this is the core principle of vector images and why it uses DXF files.
If you want 'thinner' lines, you would need to either use a font that is fine, or offset the polylines inwards after the text is converted to that there is less 'fill' area - the "pen" will make a double pass over some areas, but what do you expect.
To make it look like it will output, change the "pen thickness" in the drawing to match the tool on your engraver: any "gaps" will be visible.
If you want the internal area to be engraved out, then you will need to fill it with a fine "hatch" pattern (remember to scale it properly, and changing the pen thickness will not alter what the fill looks like - neither will zooming)
The people I know who use vinal cutting machines use CorelDraw rather than a CAD package (I think you can pick up V8 for much cheapness and it will do everything you need)