Can you simply use gift vouchers from, for example, a new Ps4 game available in the library if you are the first to borrow this game?
The PS4 game is owned by the library, and so is the enclosed voucher, I assume. This voucher was probably not part of the sales contract between the seller of the game and the library, but a promotional gift will also become the property of the recipient.
But if such a voucher is only scattered among people to attract attention, to seduce people to try out a product,
then the "gift" is more likely to be directed at potential users of such games.
A voucher for another game that the library could lend should then be given to the library.
The library can hardly use a voucher for things like "two weeks for free trying out how the new online game XY can inspire", however - their employees are hardly allowed to pull something like that off themselves: they could at most let it expire - or donate, for example to poor children.
So right-pragmatically speculated. In legal dogmatic terms, however, the library is the owner of the voucher.
But it doesn't cost anything to ask there ;-)
