Hi Jim
The steps you are taking are correct as far as I can see and they do work correctly here.. The section on the timeline SHOULD be the bit that exports. (Exporting time and size depends on your settings )n but it should still only be the bit you isolated. I know it's of little consolation but I have duplicated what you did with a 1 hour 4Gb single MPEG4 clip and extracted a 1 min section near the end; it exported OK here.
There are a couple of things however I notice regarding the file you exported.
The ORIGINAL clip in the clip bin shows the first frame as is normal in the clip preview......Note the player in a distinctive white shirt.

The first frame you isolate in the preview is this ...... It's obviously not the frame above and is, as expected the frame where you cut it... Nothing abnormal here...

Now, although it's rather small and somewhat fuzzy, the frame (the first frame) of the exported clip (I assume it's your exported clip.....which appears below for only a fraction of a second in your video) does not show the first frame of the original clip as I would have expected if that had been erroneously exported. It seems to show the correct frame of the start of the isolated segment which would be correct..It does look like the frame above. It's certainly not the initial frame of the original clip with the prominent player in white.

Disregarding the actual SIZE of the export which can be simply due to the export settings etc. It does seem from this that the export IS possibly correct. Are you certain it isn't your short segment despite its apparent size?
What actually plays when this file is shown?
Nat