I've found three solutions.
Play the exported video in a player that can compensate for the problem. On macOS, I've found the IINA video player to work <https://iina.io>.
Export it from EyeTV using one of the export formats that re-encode the video. For example, use "Apple TV HD 1080p" or "HD 720p".
Re-encode the exported video using a program that can compensate for the problem. I've found HandBrake <https://handbrake.fr> and Shutter Encoder <https://www.shutterencoder.com> to work.
Of course, unfortunately, re-encoding can take a long time.
The "HD 1080p" export format in EyeTV does not perform re-encoding. So it is very quick, but it may have the stuttering problem.
Out of all the common export formats supported by EyeTV 3.6.9, I recommend using either "Apple TV HD 1080p" or "HD 720p". They all produce H.264 video files. But for 1080p or 720p output, those two produces slightly smaller files. The formats "Apple TV", "Apple TV HD" and "iPad" also produce 720p. The "iPod" format produces lower resolution 480p, and the "iPhone" format produces an even lower 360p, so it is unlikely you'll want to use them.
This problem appears to be causes by incorrect frame rate information in the video stream. In my case, roughly each 5 frames has 2 repeated frames, one of those repeated frames is a copy of one of the earlier frames is from a few frames earlier. Hence, it is out of sequence and causes the video to stutter. This is similar to what telecine pulldown does to convert frame rates.
