Closing them would help the developers, as sites like GitHub make it much easier to track and act on issues.
However, I don't think we should/can assume that every Stack Apps user has an account on sites like GitHub -- they may not be developers and are just casual users. Although it's easy to make an account, I don't think we should force them to!
If we did close the questions, they could comment but then they would be limited in the details they can provide because of lack of space. I often have users post issues/bugs in comments and it makes it a lot harder to track than an answer would be.
How about a 'mod message/notice' kind of thing like they have on Meta sites just to bring to the attention of users that ideally issues are posted elsewhere? This feature request on Meta would be perfect IMO: Allow Moderator Comments with the Prefix "Moderator Note" to show up in collapsed comments (main Meta site).
@Brock mentioned that there is a way to add post messages without locking the post, which would be ideal. Screenshot courtesy of @Έρικ:
We could ask a CM to add another pre-defined message for our use case if we had enough posts to show it's needed. A possible message:
The post author has requested that all bug reports and feature requests (and questions?) are posted on [sitename]. Please consider doing so to help them manage issues!
Another possible solution (which would again require something 'extra' for Stack Apps, so I'm not sure if it's feasible) would be to show an alert similar to when users post an answer, like is currently shown when you post 2 answers on the same question:
However, the message would be something like:
Are you sure you want to add an answer?
This post author has requested for issues and feature requests to be posted on [sitename]. Please consider doing so if you can, as it would make it easier for them to manage