Xbox 360 GWG free titles will carry on working on both consoles.
Xbox One GWG free titles require an active Xbox Gold Subscription. Discounted titles will still work.
The FAQs do not stipulate about the games, but stipulate about the consoles.
On Xbox One, you will no longer be able to access your Games with Gold titles if you cancel your subscription. However, if you decide to renew your subscription at any time, you will be able to access and play your previously redeemed Games with Gold titles again.
On Xbox 360, any Games with Gold titles that you redeem as an Xbox Live Gold member are yours to keep, regardless of whether you continue your subscription.
The above suggests to me that any games on the XB1 (regardless of whether they are XB1 of 360 games) claimed via GWG will be unplayable without an active sub. Whereas if you are using a 360 you can continue to play the GWG games when there is no active subscription.