The GodKing is the owner of the site, or its administrator, or any sysop with ultimate power. He uses his authority a lot, but often in subtle ways. See also Pointy Haired Boss for some of the important attributes of typical GKs, and God's Eye view for why PHB and GK are limited views.
Some people think this is fair (especially when the GodKing is the "creator of the site", or the "owner of the server" - see capitalism) and good (because he can ensure that certain guidelines stay undisputed). Others think it is oppressive and limits the quality of participation, since no one wiser than the GodKing will be heeded in its decisions.
There are also calls for representative democracy to form a kind of constitutional monarchy model of wiki civics - see faction for an initial attempt at this. There are also calls to anarchize most large public wikis and have them run simply by whoever shows up, and to socialize it by having Sysop Vandal point of view dominate - only those who have technology power run it.
All of politics as usual seems to get involved whenever any question arises about the role of the founder/ GodKing.
 minimizing the damage
To avoid becoming oppressive, the GodKing could stay away of his site if possible, be transparent in any of his decisions, and empower others whenever possible.
GodKings should avoid threatening or scaring away editors, as they would resent it, and perhaps take revenge at worse, or stop contributing.
 relation to hard security
The GodKing usually owns or has the trust of those who own the infrastructural capital of the web service providing access, even if it is to a public resource, e.g. the GFDL text corpus. This role is essential to any hard security regime as it provides some cover for a sysop power structure whose acts would otherwise be sysop vigilantiism.
Because even soft security schemes rely on sysop vandalism to "discourage trolls, such a ruler is usually considered a usurper by such minority authors. However the community point of view will almost always strongly reflect the GodKing view, since members of that virtual community are selected only from those who the GodKing accepts. Accordingly to retain power, the GK will almost always advocate the Sysop Vandal point of view.
This POV is simply hard security masquerading as soft security, using bullying, lies, and propaganda and the selective use of ad hominem deletes and so on to control information about wiki governance.
Most wiki management ideology, e.g. the wiki way, considers the GodKing rulership paradigm to be hopelessly primitive. Indeed, it seems to have gone out with the pagan Caesars. However, in the case of Wikimedia, a godking clearly controls the project and does damage to it, as a means of demonstrating power to control it.
See New Troll point of view for the most diametrically opposed POV to that of the GodKing or his minions. This mindset seems to apply dialectics to dealings with troll-sysop struggle and its implications for wikis.