To answer your question, no, the web app policy cannot be codified in the site rules beyond the extent that has been done. And that's by design. You linked to one of the central discussions on the subject (there are endless other Meta discussions, about the subject in general and specific cases). The discussion you linked to alludes to why it isn't further codified.
All of the SE sites are designed to allow growth and evolution, both organic and through policy changes. Every day, there are plenty of examples of old questions in the Close queue, as off-topic, that were considered just fine at the time they were posted. Things are codified in the most general possible terms to allow for community interpretation, and evolution that doesn't require regular modifications to the site's guidelines.
An unfortunate side effect is that what serves as guidance isn't documented in one spot as "the rules". It's a collection of community discussions in Meta that provide the interpretation of the broad guidelines in the Help Center.
But to try to summarize the web app guidelines as of now, synthesized from Meta discussions and a lot of time in the review queues, here's my understanding of the dividing line:
- If the application software is installed on, and runs on, your computer it's generally on-topic (assuming the subject matter is on-topic).
- If the application is an online service that functions like an application, it's off-topic.
- Online extensions of your hardware in the nature of storage, or virtual hosting of your PC software, are generally treated the same as running on your own computer. Technical questions that would be on-topic for your own computer are generally on-topic; the "business" side of interacting with the service provider, and the mechanics of dealing with their infrastructure, are off-topic.
- Questions regarding a web-based application interacting with your computer or local software can be on-topic, similar to phones being on-topic to the extent that the question involves connecting to or interacting with your computer (issues like moving/transforming data; think "web app as a peripheral device" for a question that is PC-centric). How to accomplish something in the web app would not be on-topic just because you use your PC-based browser to interact with it. Questions about the browser, itself (including installed extensions), are on-topic.
- Clearly off-topic examples: websites or web services like Facebook, Twitter, and WordPress (specifically listed in Help Center), Google Spreadsheet and other web apps; topics for which the tag indicates that it is off-topic (and the tag wiki excerpts can educate about the rules underlying them); questions about how to use web-based services, like search engines, from your browser
- Gray area example: Office 365 Online version is often, but not always, migrated to the Web Apps site
- And, of course, topicality applies only to the question; an answer can suggest an "off-topic" solution to an on-topic question. Also, exceptions for borderline cases are made at the discretion of the community.