Which ticket are you trying to get exactly? I’ve just checked on the LNER app and they issue an Off-Peak Day Return from Bournemouth to Gatwick Airport via Barnham on an eTicket.
I can’t actually find how to access Virgin Trains Ticketing without signing up for Virgin Red, but I noted the word “SplitSave” in the support documentation I found for it, so I’m assuming it uses Trainline for the backend, and interestingly the same ticket I tried above is only issued by Ticket on Departure on Trainline.
Trainline’s database of what format tickets can be sold in can be inconsistent with what it’s meant to be - this issue also extends to any ticket retailer that uses Trainline as its backend, such as Greater Anglia who don’t offer this as an eTicket.