This isn't a remote root code execution bug, but it shouldn't be taken lightly, either. The exact environments where this bug would be applicable (locked-down) are the environments that could suffer severe damage because of an escalation issue.
The thing is, though, local privilege escalation isn't new, and it isn't novel. This is one in a long string of many, many similar bugs across most every major platform. It's completely unremarkable except for the reluctance on MS's part to patch it in a reasonable timeframe.
It means that every user effectively has root privileges. Which means that every user can eavesdrop on other users, view their saved data and files (unless encrypted on disk), intercept their network communications, impersonate them, steal their passwords (system, application, external web sites).
How bad that is depends on your particular use case. But for pretty much any setup where security is a concern or there's any sensitive data at stake, this is a very serious issue.
With the set up of Windows servers I've seen, only the admin logs in anyway. It's not really used as a "multi-user" system per-se, where you get different users logging in at the same time. It does happen, but it's not common.
Could you clarify, though: do you mean to say Windows isn't as vulnerable because of cultural reasons (i.e. Windows systems aren't multi-user usually) or because of technical ones (they support something like SELinux out of the box)?
Are Microsoft downplaying or is this genuinely quite minor? The article discusses a disgruntled employee and since all their money comes from Enterprise presumably disgruntled employee can cause major damage is a pretty huge problem?