This is a bit unusual and I can't reproduce it on my end. I tested as a user in a free portal without export permissions but was still able to see this option.
I am a super admin and have the same issue. I am trying to export data for specific ranges (quarterly). I am able to export data from out-of-the-box reports by when I customize the date range for the data I need, the option disappears. Please let me know if there is something I am missing.
This is a bit unusual and I can't reproduce it on my end. I tested as a user in a free portal without export permissions but was still able to see this option.