I'm not 100% certain, but I think those door-close things are designed to cope with doors like that. Those I've encountered in the past have had to be held open with something pretty sturdy otherwise they closed whether we wanted them to or not.

Wildcard_sej is probably right about the insurance aspect - you could point out to the landlord that if the building's not secure his building and liability insurance are void. That last bit may or may not be true by the way - but chances are the landlord doesn't know either... :)