For me, these files also exist for a handful of shows. ".vhdresolution" files are not required to properly play a show. I think iStripper creates them in situation where they are neccessary, but what are those situations? I'm not sure. Maybe it has something common with default resolution that you choose in Settings? Let's see...
Yes, it has. Try this: go to Settings, make sure "Advanced settings" is checked, scroll down to "Downloads" section and set your default resolution to, let's say, 720p. Now go to "My collection" tab and choose any of the recently downloaded shows. From the dropdown list select resolution different than your default one, let's say 3K or 4K. The ".vhdresolution" file has been now created. It contains info about selected resolution, not the default one, but the one selected for this particular show.
The same works the other way around. If the default resolution in Settings tab is set to 3K (or 4K if you're premium member"), but you choose different resolution for particular show, the ".vhdresolution" file will be automatically created. For example: @Evaneself has access to 3K shows and I can assume that his default resolution is set to 3K. But he choose to download Diana's shows in other resolutions (720p and 1080p). That's why iStripper created the ".vhdresolution" files for the other resolutions.
-- EDIT --
More notes:
1. It seems that ".vhdresolution" is created by Istripper no matter what you have set in Settings. Just open details for any show, mess with the "Resolution" dropdown list and this file will be created. It is that simple.
2. If you choose 720p, the ".vhdresolution" file will be empty. It looks like this is the default resolution, so iStripper doesn't write data to ".vhdresolution" file if 720 is selected.