Did you try https://whispersystems.org/ ? There is a desktop version but it doesn't support voice: https://whispersystems.org/blog/signal-desktop/
'Desktop version':
- it is a Chrome App (arguably not a desktop client?)
- it in (restricted) beta, aka not available
- the beta requires (acc. to the link you provided) "your Google account email"
You can make voice calls with Signal, to other Signal users.
Given that they replaced Lync/Skype for Business™ I assume they ideally want a comparable offering: Voice and chat for a number of platforms.
Signal would give you voice on mobiles only and chat on mobiles only, ignoring the Chrome App beta thing.
I might be entirely wrong, but I assumed that the GP chose Telegram for now due to the multi-platform support (chat on all platforms, replacing Lync/Skype in that regard completely). If that is correct, moving to Signal would be a trade-off, exchanging multi-platform support for voice calls. It's not a solution, it's a different subset of Lync's/Skype's feature set
You can go the other way around and "build" it. Just clone their repo and point Chrome to the cloned directory so that it knows that there's an unsigned extension there. Done.
Once on of your contact uninstall Signal without disabling it first, you will have to long press the send button EACH time you want to text them. Annoying as hell, it made me stop using Signal.