Where did you get your information?
I didn't need to go far. I checked the version on the Mountain Lion system that I have here.
(I have full system installs that I keep updated, on a couple of drives, for every system version from Tiger/10.4.11 to current Sierra. So it's easy to see what app versions are available on each system version.
You show a variety of facts, but you perhaps did not realize that each version of OS X has its own version of the App Store app. For example, you can't run the Snow Leopard App Store app in Lion, and you can't update the Snow Leopard version to a newer version, unless you also update the OS X system itself.
Each version of the App Store app, which started late in Snow Leopard, is part of its respective OS X/macOS installation.
For example, the Snow Leopard version cannot run on Lion, and there are no updates to the version included with each OS X system software version.
Bottom line: App Store has been available since Snow Leopard, and each updated OS X system since has also updated the App Store app (among other native apps in the system), and many of those apps will NOT run on newer (or older) systems.
What does that mean for you, as a potential user of Snow Leopard (or Mountain Lion/whatever)?
Each system version has its own respective "stable release" version of the apps installed by that system, including the App Store. There has not been any updates at all to Mountain Lion, since the final security update for Mountain Lion, which was release in August 2015. That would be the last update that might have affected the software update software, but I don't know if that actually changed anything about Software update, just guessing.
If you need to discover if there are updates for your system, run Software Update.
OK, Software Update has also not been available as an app since Mavericks (I think), and updates are now only provided through the App Store. That's one function (software updates) where Sierra has completely changed since Snow Leopard.