While Remote Utilities allows you to switch between already existing terminal sessions, it has no means of creating terminal sessions or being run as a terminal server. It's a different class of software with different licensing.
I'll continue here so that the full context is available to other support staff.
Ok, I tried to connect but with no success. However, I couldn't ping the GMS' DNS name either. I have a question - is GMS in the same local network as the Host? That could explain why the Host/Hosts had easily connected to the GMS and were shown in the idle list. It can be so that the GMS is misconfigured or is simply not accessible out of the Internet by the DNS name you use. I assume that the computer with the GMS installed doesn't have an external IP address and is only available via a router. Did you set up a port forwarding rule on the router then?
I recommend you to check back the "Default server" checkboxes on both ends and try to establish remote connection using our default servers (you don't even have to change the ID, although it's recommended to re-generate it just in case). In this case you will at least get a general idea of how the program works, and then you might want to try more advanced options such as the GMS.
First, let me elaborate on three possible connection types:
1. Direct connection by an IP address or DNS name. In this case no intermediary server is used. Viewer connects directly to Host.
2. Indirect connection by ID: hosted by us. This is the simplest setup - just follow this tutorial to get everything up and running in seconds. You don't have to change any ports.
3. Indirect connection by ID: hosted by you (GMS). You point both Host (Settings -> Internet ID connection settings) and Viewer (selected connection -> Properties -> General tab -> "Change" button) at your GMS. Note that for Host this setting is global whereas for Viewer it's on a per-remote-connection basis, that is you can have records in your address book that use different types of connection. Once you specified your GMS instead of the default ID server at both ends, use the ID of the remote computer in order to connect just like you would do if you used the second type above.
I would recommend you exactly follow the GMS manual as it explains everything you need to know for this advanced (yet powerful) option.
Don't hesitate to write here if you didn't have any success with configuration.
I've got to say, so far I'm really liking Remote Utilities (and I've used gotomypc and [censored] for years). Still figuring out a few things, but that's normal.
Thanks for using Remote Utilities! Don't hesitate to share with us your suggestions right here on the forum. Though we have certain priorities and implement new features in the order of most impact/importance, we always include user suggestions to our wish list and further to the roadmap if they fit our product's general paradigm well.