I've managed to do this with GDAL rather than tippecanoe. It's possible to define a custom tiling scheme there. This works with EPSG:4326 as well, even if the coordinates aren't in the range of ±90° latitude and ±180° longitude. Therefore, this is a viable option also for non-geographic maps.
Tiling scheme can be given to the GDAL MVT driver with the dataset ...
Still not sure if that's the optimal workflow to get from CSV to MVT but I ended up using GeoJSON as an intermediate step. This can be done easily with GDAL/ogr2ogr:
CSV (geometry saved in column named geom, in WKT format):
id name attr1 attr2 geom
1 garden1 green round POLYGON ((30 10, 40 40, 20 40, 10 20, 30 10))
2 garden2 ...