Hi, I'm afraid accessing it from the cloud is exactly what they have done. I have seen this in another university where NVivo can now be only accessed via a browser by logging on to a Citrix server in the university. They may well be breaking licensing agreement depending on how they are licensed and how many people they grant access to this server. The data file still sits on the local computer but the software is accessed on line.
I'm afraid there is no solution other than acquiring a license for NVivo your self or kicking up an almighty fuss on campus. It strikes me like an IT professional who is administrating the network may be taking a lazy approach to granting access to students for software licensed by the college. NVivo is set up to be a local installation and this can be time consuming for administrators.
You could inquire from the software developers QSR International, if this arrangement is breaking the terms of the university licensing agreement. If it is, you will find QSR will act quickly to address this with the institution (https://www.qsrinternational.com/support.aspx)