I'm not going to download the GPX file - because the link requires you to sign up for something else.
Basecamp does an excellent job of reading badly formed GPX files and tidying them up so that incorrect lines are discarded and the file contains only correctly form GPX tags. Often with dodgy routes or tracks loading them into basecamp and resaving them cures the problem.
But basecamp also has a facilty for reducing the number of points in a file.
Double click the track in Basecamp and a dialog box opens up, with a number of options at the bottom.
Filter, Invert, Create Route, Create Adventure, Print.
Choose 'Filter' and this pop-up appears

- Filter.jpg (22.58 KiB) Viewed 489 times
You can filter it in different ways - all of them mathematical.
Maximum Ponts - if it has 10,000 points and you specify that you want a maximum of 1,000 then it will keep one point and remove the next 9. and repate that all the way through the file.
Uisng this, you can easily half the number of points in the track.
On a route with straight roads, that might make a significant difference - so specifying a longer distance between legs might be a better option. It means that your track my chop off corners - but if you are specifying (say) 300 ft between points that isn't too bad.

- Reduce Track Points.jpg (24.12 KiB) Viewed 489 times