Unfortunately, the export to route option was not available for me on that activity, which is incredibly annoying. However I did find a nice strava labs tool which let me create the GPX file.No, @si_c is right, you can't directly export a gpx, but you can create a route from anyone else's ride, and then get the gpx from that**.
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But an useful alternative is using the Strava route builder. https://www.strava.com/routes/new It creates routes using popularity, so it will find you roads that cyclists choose, so generally you can be happy with the conditions. I raved about it a couple of years ago.
**I bet this option becomes premium once the route build goes out of beta.
See http://labs.strava.com/gpx-to-route/ worked a treat, saved the activity to me routes, and I was able to download from there. If a non-premium user can check if it works for them, might be worth keeping in mind for the future.