For the purpose of the site, questions about NGOs are on topic if the NGO has a political purpose. Thus the Nation of Islam is certainly a political organisation, and it campaigns on matters of civil rights and black liberation that are directly relevant to US government policy. The question linked above concerns the political beliefs of the organisation.
On the other hand the IOC is not concerned with influencing the policies of governments. There may be a lot of "office politics" within the IOC, but it is not a political organisation. Therefore this question is off-topic. It would be possible to ask "Does the IOC promote democracy when awarding the games" since this asks about political activity of the IOC.
The question about anonymous is too broad. It can't be answered in a simple and verifiable way.
NGO questions are allowed, only if they are concerned with the relationship between NGO and governments, or the actions of NGO as affecting policy. This is the same idea as when questions about individuals is on topic. The individual has to be involved in politics or attempting to influence policy, and the question has to be focussed on that involvment to be on-topic.
The help pages should be written to clarify that questions about NGOs should relate to governmental policy. The internal politics of NGOs is not on-topic.