According to Strava policy they have removed the possibility to sync your workouts with other apps that are their competitors. As you have noticed that Strava also allows to organise virtual challenges, so they do not give us permission to sync data with them.
So you have two options:
1) Manually download workout GPX file from Strava and upload it to DistantRace. You must login to the web version of Strava to download the workout GPX file.
2) Record activity with other services that are connected with DistantRace.com. In case you need to record your workout on Strava as well, use both services.
3) Record activity on a service that can be paired with Strava. For example Suunto (you can record activity with Suunto app):
Suunto app -> Profile - Partner services -> Strava
Distantrace.com -> Profile -> Connections -> Connect Suunto
Record your activities with Suunto and it will send the activity to both Strava and DistantRace.com