I see contradicting claims.
It doesn't really make sense to talk about whether "short-term memory" or "working memory" decline first, so I think there is some confusion of terminology. It seems the reference comes from the second linked article, which colloquially suggests that 'short-term' face memory declines before working memory. In modern working memory research, the relationship between short-working-long term memory generally is as follows.
- Short-term memory: A few seconds.
- Working memory: As long as consciously maintained.
- Long-term memory: Permanent.
This ontology goes back to Baddeley and Hitch's work on the modal model of working memory from the 1970's, and has largely been maintained in subsequent item-based models (how most people think of human memory today).
Short-term memory isn't used as a formal construct very often in memory research anymore because it's a rather vague term, though I think perception researchers still use the term when they don't want to tread too far into memory theory. Instead, it's simply used colloquially as any means of remembering something over short time scales.