Is there a way to configure a list so that a user has read/write permissions for a list through REST, but that same user is prevented from going to the list in SharePoint itself and editing this list from there?
Nope. The best you can do is obscure it.
For example, you can edit the New and Edit forms of the list, using audience targeting to prevent the users from accessing the forms.
You can also remove their ability to create or edit public or personal views, then ensure that the public views don't display any items (otherwise they'd be able to use datasheet view to edit list items).
Remove the ability to add personal pages and webparts, and change the NewForm.aspx to either redirect on load or disable the Save button. Also, disable offline clients. That way, the only way users can add/remove/change is programmatically.
One catch is using the datasheet view--which you may be able to write some CSS to remove/disable the button. To normal, non-techy users, this is an acceptable, but not foolproof way of restricting.