What is the aspect ratio of the video? The wide screen release is not a standard 4 by 3 or 16 by 9. It is something like 2.39 by 1. That may be the cause of the display issue..

Do you see this on another commercial DVD or just this one?

What is the maximum resolution for that Surface Pro 3? .
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BoilerPlate: To posters who ask for help -- it is nice to thank the volunteers who try to answer your questions !
Anything I post unless stated with a reference is my personal opinion.

The max resolution on my Surface Pro 3 is 2160 / 1440
though this screenshot was taken on my smart tv which is 1920 / 1080. The DVDs aspect ratio is 2.35:1.. it says it is special widescreen presentation with letterboxing.

So I guess there isn't much I can do to remove the letterboxing without distorting the image.

Looks like it. Does the DVD have any other options about playing it that are not wide screen. .
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BoilerPlate: To posters who ask for help -- it is nice to thank the volunteers who try to answer your questions !
Anything I post unless stated with a reference is my personal opinion.

I know this is an old post but you might try double left clicking on the image and see if it will fill the screen.
It may only fill left to right with black bars on top and bottom.