If you open them in a browser when you're offline, you won't be able to load/read your messages (yes, I know about HTML5 manifests for offline data... but that's a mess), but with Signal you can.
Moreover, being able to vet/verify the updates (which you can apparently even block altogether) before running the app is of paramount importance for a secure app like Signal.
With a run-of-the-mill webapp that's also impossible.
Again: tradeoffs. I'd prefer if Signal desktop was built on something different, but I still happily use it as is everyday.
I won't install Chrome just to host Signal extension.