By a Private Military Company, a Paramilitary Organisation or even a part of the regular Military

What is a mutiny?

Wikipedia says: Mutiny is a revolt among a group of people (typically of a military, of a crew, or of a crew of pirates) to oppose, change, or overthrow an organization to which they were previously loyal.

In this case the organisation is the Russian State.

The size of the group mutinying must be at least 500 people. (this could either be the headcount of the organisation (if the organisation is generally involved in the mutiny) or the reported number of participants in the mutiny)

"What if Russian troops refuse to follow orders?" (like the French mutinies of 1917)

"These kind of situations will be hard to pre-emptively fully cover, but the 'spirit of the question' is that the "mutiny" should involve an attempt* to force leadership change on the organisation they are mutinying against, rather than simply a refusal to follow orders likely to lead to death. Of course, often such a refusal swiftly leads to rather more active resistance.

In the case of the French mutinies, from brief reading it seems that their demands did not include (perhaps surprisingly) the removal of Nivelle from his position, so in a hypothetical exact repeat I'd resolve NO, barring persuasive expert arguments in the press that there was an attempt to force leadership change."