Well, it would depends on what exactly "draw" means.
If you can somehow programmatically calculated each vertices of the polyline (without the lead of user moving the mouse cursor) and drawing it at once, then you probably can do it with VBA.
if you want to the SAME thing as the video show (a dynamic polyline following the mouse cursor's move, which may trigger some calculation when the cursor is near/at particular entities to determine where the polyline goes), VBA is not able to do that. It surely can be done with AutoCAD's .NET API (or ObjectARX C++, if you choose), though.
For example, one of the articles in my blog shows how to visually drag the mouse cursor along a polyline (a known path) with Transient Graphics. The code in that sample can be modified to do what you want: instead of moving along AT the path, the dynamic polyline can be set to an offset to the path; and the code also need to calculate the path when the cursor is near/at something. At the end of dragging (when the cursor is near a predefined point, or user click a point, the dynamic polyline drawn as Transient Graphics would be replaced by a actual drawn polyline.
Well, if you program in AutoCAD .NET API.