Does this plugin exist? If not, does anyone know of any alternatives besides coding our own?
We ran into something similar with one of the CartThrob listed payment processors. It was listed in the docs, but the processing files were missing for that specific gateway. We reached out to CartThrob support and were emailed the missing files 24 hours later. This sounds like a similar situation so you may try to set up a support call with them directly.
I'm afraid I don't have a particularly positive answer...
The "Buy" button on the documentation now goes to a blank page and there are no mentions of it on the main Cart Throb website. I think you can consider this one dead.
Because has CartThrob included first-party gift certificates since 2012 it looks as though there was never much demand for a third-party solution and so there doesn't seem to be any alternatives on the market.
A popular alternative to CartThrob, Exp:resso store doesn't have gift certificate support either at time of writing, although it is a candidate on the "Feature Requests" voting page at https://exp-resso.com/support/feature-requests.
Brilliant Retail doesn't have gift card support either (unless you want to make single-use coupon codes manually - in which case all 3 of these platforms should accommodate).
Unfortunately ExpressionEngine can be a bit lackluster when it comes to eCommerce websites. Typically it works well for sites with a few products and very basic functionality but when you introduce advanced digital products, certificates, delivery tables, tax tables it lags behind other solutions such as Magento or Shopify.