You are correct about it being shot on a cell phone – at present the top comment on the video is from @RickAstleyYT and says:

My wife Lene and I shot this video on a phone in Denmark, in a forest beside a beautiful beach. The song in essence is about how there is so much technology out there pulling and pushing us in our daily lives, that we need to remain human in this fast moving world. The idea of making a video simply, somewhere beautiful and real like this resonates with me, and I hope it does with you too! Rick x