Hi Alexandra,
Where are you trying to download the data from? ArcGIS Online? I would also be interested in your workflow, to see if I can reproduce the "Unable to import this shapefile" message on my end.
Based on the information provided, it sounds like you are attempting to upload or add a spreadsheet to your map. If you want to do this, you do not need to zip the file. When adding a zipped file to a webmap, the webmap is assuming it is a shapefile. Since your zipped file contains only a CSV/spreadsheet and not a shapefile, I suspect this may be causing the error message. You can add the spreadsheet to the map by simply by saving it as a CSV, then adding that CSV to the map.
Add layers to maps—ArcGIS Online Help | Documentation
Best,
Megan