Tarun and Amandeep, thanks for your suggestions. I got it to work by fiddling with the firewall settings.
My feature request remains, because I doubt that I'm the only one experiencing firewall issues, or that this is the last time I encounter it. For the record, indeed it was the multicast DNS package (which is the network traffic that ensures service discovery for the server) that somehow did not reach Enpass, and connecting to the server (on another computer) worked just fine. So indeed, giving me an option to manually fill it in (like I could with my phone) would still be useful as a backup option.
Thanks for considering this.