Hi,
thanks for your post, and sorry for the trouble.
I see what you mean, but unfortunately, this is not directly possible like that. TablePress does not have a feature where only individual rows can be edited by a user.
However, I recently implemented a solution for this in a slightly different way:
You could give each of these users their own table (with just a header row and one row with their data). Then, you could use the Advanced Access Rights premium feature module that is part of the TablePress Max license plan to assign the individual users editing rights to only their own table.
Using a special Shortcode from a small piece of custom code (which I would provide as part of the direct priority support that comes with TablePress premium licenses), you could then construct a big members directory table, which would pull in the information from the small tables that these contributors can edit.
In addition, I would provide a custom solution that would send you an email notification with the new data that these contributors entered in their tables, when they edit them.
If this approach and getting a TablePress Max license are of interest for you, please feel free to to get in touch via the email address from the bottom of https://tablepress.org/pricing/ so that we can discuss this further.
Best wishes,
Tobias