Aaagh! Not again! I used to run a railway station and I've probably written hundreds of times on AB that people should NEVER book with The Trainline! They CAN'T offer any cheaper fares than those that are available via the National Rail website. Customers can actually end up paying MORE when using The Trainline due to their booking fees! Further, I got fed up of having to explain to customers that the ticket that they'd purchased from The Trainline weren't valid on any train (because, for example, they'd been issued for travel on Operator A's service but using a ticket that was only valid on Operator B's trains) and that they'd have to buy new tickets at the station.
So, for the umpteenth time, I'll type it out yet again: DO NOT BUY TICKETS FROM THE TRAINLINE!!!
Your own National Rail link contains this wording: "Check with your ticket retailer to find out if they are participating in the Book with Confidence scheme". I suspect that The Trainline will argue that, while they've agreed to go along with much of the scheme, they've not adopted it in full, meaning that they've opted out of the bit about getting vouchers for future travel.
Try a phone call to 0333 202 2222 though, to see what they say. Lines are open from 0800 to 1900 daily, with calls charged at the same rate as those to 01 or 02 numbers are from your phone. (So if, for example, you've got spare 'included minutes' on your mobile, that means that your call will be free).