That's actually a very concise yet accurate summary of the rule which is widely, almost universally, misquoted and misapplied.
As in this article, for example. Short term memory lasts for seconds. The mnemonic tricks discussed in the video are not for short term memory.
Mnemonics are interesting stuff though. Memorizing the order of a pack of cards (once you know the techniques) is not hard and worth doing just to surprise yourself. Of course doing it really fast or doing 10 packs is another matter.
I don't really see the connection to story telling except in the most tenuous of ways, though I think that is also a powerful technique for delivering presentations.
I see how that sentence is ambigious. I meant that you have it correct. The two key elements being "short term memory" and "items (variously defined)".
This article thinks it applies to long term memory, and most people don't realise you can 'hack' this by chunking 'items' into bigger 'items' (e.g 7 two digit numbers have 14 digits total).