As far as I can see from the discussion there, by unit level they mean the level of the panel variable. What that is depends on your study. It might be firm or individual or country or whatever your panel variable happens to be.
The panel variable is the variable that dictates the spatial dimension of your panel data. E.g if your panel consists of observations on firm level across multiple years, firm is the panel variables. However, if your panel consists of observations on individual employees across different years, then even if you have firm identifier your panel variable would be employee and so on.