Is this question off-topic?
That question is off-topic because it does not depend on the expertise of professional software engineers. It can apply to many professions - 20% time can be used by an electrical engineer, a software engineer, or a graphic designer.
Based on the current faq, it would be off-topic
The current faq states that the site is for conceptual questions about software development, which includes things like design patterns, architecture decisions, data structures, etc.
Career advice and workplace issues are explicitly off-topic.
The site used to allow some career or workplace advice questions providing the answer required a programmer-specific answer and not an all-careers-specific answer, however that no longer appears to be the case since the example on-topic career question provided in the linked meta post of the faq for career advice questions has been closed.
If I am mistaken and they really do allow some career or workplace advice questions providing the answer is specific to programmers and not all careers, then I would consider the question would be on-topic. The question itself does not apply to all careers (not all careers find it beneficial to have a 20% time rule), and so therefore the answer does not apply to all careers. If "Freelancing and Business Concerns" are on-topic here, than I would expect questions on how to implement a popular development work strategy to also be on-topic.
It is on topic.
The FAQ provides nine on-topic categories and seven off-topic categories.
As the top answer to this question shows, the 20% time -- perhaps this is an insight unexpected by the OP -- is clearly not a workplace perk, but an important element of a software development process. How it is understood and implemented affects the performance of a software organization, its agility, and the quality of their products. As such, this question fits into "development methodologies" or "software engineering" on-topic categories and is therefore on topic.
As for the seven off-topic categories, this question clearly doesn't fit the last six categories and, as the top answer clearly explains, is not a "general workplace issue."
The closing moderator's suggestion that this is more of a Workplace question is most certainly misguided. This is very serious software engineering question -- again, its seriousness may not have been fully anticipated by the OP -- and is a useful contribution to the Programmers' site. It belongs here rather than next to the following: