If I understand you correctly, in particular the "zelfstandi is similar" bit, then maybe you can do as follows:
library(dplyr)
data %>%
group_by(zelfstandi) %>%
summarise(total_shape_area = sum(Shape_Area))
This will sum the Shape_Area for each distinct value of zelfstandi (by the way it looks quite weird that this variable is a mix of integers and strings)
This is the data I got, but I could change the "a" to a number as well if that makes things easier.
Using your code gives me the following error
no applicable method for 'group_by_' applied to an object of class "c('SpatialPolygonsDataFrame', 'SpatialPolygons', 'Spatial', 'SpatialVector', 'SpatialPolygonsNULL')"
Looks like your data is not a "regular" data frame which the dplyr verbs are meant for. Can you convert it to a class data.frame or tibble (which inherits from data.frame)?