Well, that was kind of an over-arching sentence, that Snappy has those advantages-- they don't all come from transactional updates. Transactional updates applies to the "faster" and "more reliable" parts.
With the normal Ubuntu (Debian) packages, you only install one version at a time. If you install version 1 of package foo, and version 2 is released into the repos, then you update to version 2, which effectively uninstalls version 1. If you don't like version 2 (or it was broken), you have to essentially uninstall it and install version 1 again.
In Snappy this changes a bit. If you install version 1 of package foo, and version 2 is released into the store, then you update to version 2. However, version 1 remains installed, it's simply deactivated. If you don't like version 2 (or it was broken) you can roll back to version 1 immediately, without downloading anything. You can see how this would be faster and makes for a more reliable system.
As for why Ubuntu doesn't adopt the Snappy approach, well, that's what Ubuntu Core is! Ubuntu Next is now also based on Snappy. It's just that Snappy is still being developed when it comes to GUI-based things (note that Ubuntu Core is CLI-only).