Hello Szabina,
You can control whether ARCHICAD exports Space Boundaries or not with the checkbox you mentioned, but when it is on, it always exports 2nd Level Space boundaries (it can't export any other kind).
If your other application has problems seeing these as 2nd level boundaries, then you should contact the support team of that application first, and then your local ARCHICAD distributor, as this might be a bug.
Here's some additional information about ARCHICAD Space Boundaries:
https://helpcenter.graphisoft.com/guides/archicad-20/collaboration-guide-for-archicad-20/coordination_with_engineers/energy_analysis_applications/direct_bim_to_bem_data_export/
https://helpcenter.graphisoft.com/guides/archicad-20/archicad-20-reference-guide/interoperability/archicad_file_types_opened_by_archicad/file_types/importexport_settings-2/ - in the 'Zone Data' section
Daniel Alexander Kovacs
Professional Services Consultant
GRAPHISOFT
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