The issue is that the relationships are stored by MB in a custom table, not in a custom field, which means that Posts Table Pro (and any other solution which looks at custom fields) can't directly access the list of related posts for a given post.
I'm thinking that the easiest way to solve this would be to register a custom field which keeps (and updates) an array of the related post IDs from the wp_mb_relationships table for the post in question, and looks up the post title and URL for each, so that they can be passed to Posts Table Pro.
Can someone tell me if I'm on the right track here? I'd be very grateful for any suggestions, because I'm not that experienced with this stuff and I'm still learning to use MB to its full potential.
Meta Box supports the field post which similar to the Relationships extension. The difference is it saves the post ID in the database as the post meta like other fields. Please try to use it with the plugin Posts Table Pro.