Need your help to identify that specific condition in the which makes
the malware run only in a specific operating system.
Please note malware authors seldomly care about keeping their products updated.
For example, when assembling a ground truth for malware evaluation, there is a clear slope: most samples will work on XP, somewhat less on Windows 7 and even less on Windows 8 / 10 (not much difference here). For each step upwards, you'll lose an average of about 15% of the samples.
Often, you may be able to find a variant of a family capable of running on an newer system (but not for all families).
I figured one of the main reasons is either that the sample checks for a specific windows version or a certain exploit does not work. For example, often privilege escalation using Process Injection may fail on more recent platforms when is was developed for XP. Somewhat more advanced malware even implements different methods for different OS versions.
Please remember that malware deals with pretty low level structures of the system.
Either malware does support multi-os functionality, or it does not.
The .dll you linked seems pretty sraight forward (unpacked?) since it contains some debug information and an intact import table. Is there anything in particular you're having problems with?