Obviously he meant a geodesic though spacetime, assuming constant speed. Of course your speed does become relevant, but as long as it's positive, "space" seems broadly correct.

At least if we ignore the first 10km or so of your journey. A true straight line (geodesic) from the starting point would take us straight into a tree, hill or building. At that point the journey would end since humans can't phase through solid objects. You never reach another country.