What are electrical rings?
Rings
Your quotation has a UK source. In the UK a &quot;ring&quot; refers to a ring-main also known as a ring-final circuit. This is the typical way UK houses have provided power to wall-sockets (outlets) since the 1950's.
They are called rings because they are connected in the topological equivalent of a large circle. There are two routes back to the consumer unit (main electrical distribution panel) from each socket.

Source: Wikimedia. CCASA 2.5 Ali@gwc.org.uk. This example ring has two spurs.
Usually the ground floor has one ring-main and the upstairs has a separate ring-main. Anything larger than the average 4-bed detached might have more ring-mains.
Note that UK lighting circuits are separate and are not ring-mains, they are radial circuits. There will also be separate dedicated radial circuits for ovens/cookers, boilers and electric-showers.
Newer UK consumer units (main panels) have effectively a split power bus with an RCD for each half. So it is likely that there are RCDs between your downstairs gateway and your upstairs router.

Source: Chase Electrical.  Headings above MCBs are: (downstairs) lights, sockets, cooker ... (upstairs) lights, sockets, shower. This example has a separate RCBO (combined RCD and MCB) for smoke alarms?

Powerline
Across Different Rings
In my house I have an older arrangement that lacks RCDs in the consumer-unit. I use powerline networking between my upstairs router and my downstairs TV (it provides much better throughput and greater reliability than using WiFi in my specific circumstances) - So powerline networking can span rings.
Across RCDs
I don't know how much trouble (if any) your RCDs will cause. Anecdotal evidence suggests you might experience any of

it works but you lose around 20Mbps of 85Mbps bandwidth. or
it doesn't work. or
it trips the RCD.


What to do
I would go to a shop, clearly explain that I want to use the powerline units on separate rings each on a separate RCD. If they sell me some units for that scenario and they don't work, I would promptly return them as not &quot;fit for purpose&quot; under UK law (consumer rights act 2015).

(1)Subsection (3) applies to a contract to supply goods if before the contract is made the consumer makes known to the trader (expressly or by implication) any particular purpose for which the consumer is contracting for the goods.

...

(3) The contract is to be treated as including a term that the goods are reasonably fit for that purpose, whether or not that is a purpose for which goods of that kind are usually supplied.


Footnotes
(for Harper)

Ring final circuit test