What might be better is to offer a button on screen where the play and other buttons are. This should become available once you started watching a programme. This would work TV programmes and films.
Plex Home Theater is severely outdated and won’t get the delete functionality described in the above article. Switch to Plex Media Player or some other Plex client instead.
All models before ATV 4 don’t even have an official Plex client. And development has pretty much ceased, so I don’t think these won’t ever get the ‘delete’ feature.
The official ATV 4 Plex client already has the delete feature, AFAIK.
You just need to enable it on the server, as described in the above linked article.
Then you do a long-press on an item to get the ‘context menu’ with the Delete option.