The one world rules deal with connecting flights at the point or transfer - specifically the words 'travelling between' and international long haul and short haul flight.
The OP is asking whether they will have access at point of origin, not at the connecting point. In this case, access is allowed, but it is a BA specific rule, not a OW rule.
Ah I did overlook that, however the last point says:
You must be prepared to show your boarding pass or itinerary showing travel in First or Business class on the international long haul flight, in order to access the lounge before your international short haul or domestic flight.
So if you have a domestic flight
before your international long haul flight, and want to access the lounge
before your domestic flight, then technically at that point in time it is not
between flights, but as per that last line above, you are allowed access. That disproves your "point of transfer" theory and is the kicker.
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One reasonable interpretation of "between" is that your itinerary involves connecting from one OW (operated and marketed) flight to another, as opposed to only one leg being OW operated and marketed (and the other being not OW at all, or only OW operated and not marketed or OW marketed and not operated).
ie. see (only the) bold for emphasis.
First and Business Class customers connecting on the same day of travel, or before 6am the following day, can access the lounge when travelling between an international long haul and an international short haul or domestic flight (and vice-versa).
So it doesn't explicitly say you can access it before the short haul/domestic leg [and it doesn't say you can't] but it describes a situation where you can.
This may be a moot point in this particular situation, but for anyone else reading the thread on a later date in a similar situation, this is of value.
My guess is that this is in place for those connecting from domestic J/F to international Y/Y+, because by these OW rules, you can't access the lounge before the international Y/Y+ leg due to COS. Or for segments where J/F is not offered (ie the OP's example).