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The tool you've chosen is correct. Why it doesn't seem to work?
I made a test in similar scenario - regions and global land cover, and the tools returns a table with area (in LC raster measurement units) of each LC class in each region.
Here are possible settings:
TabulateArea.png 10.4 K
I would consider the Zonal Statistics as a Table tool. Specify the Zone Layer as the polygon file with the field of the land cover and then specify the value raster as the one you would like to survey. The output will be in a table,which you should be able to join back to your original feature class. Area is one of the statistics generated.