Clickable Elements Too Close Together waring from Google can be avoided if you ensure that neighbouring clickable elements have a minimum size of 48px x 48px. This is deemed as an accessible tap target size.
Adding margin between items would not eliminate the issue if those tap targets are too small.
By default GP sets the Menu Item Height to 60px and the spacing to 20px left + 20px right + menu text. So out the box it should surpass that criteria.
Are you getting warnings in your search console ? If you are and the above spacing is correct, then the chances are google is having trouble loading the necessary stylesheets on that page