Is nihilism the logical extreme of atheism?

[Mudhammam]

Depends upon the ideal and on what basis it is considered so.

I think you're right that theism offers no viable solution but on what basis do you think an ideal could be called objective?

It doesn't have to be defined by individuals in a particular species - the law would be applicable to all entities capable of rational consideration. It just so happens that humans are the only known species capable of it.

The rationale here is that the universal moral law can only apply to beings capable of moral action - that is, rational beings - and values, purpose and meaning derived from it would be objective because the law does not depend on any one's will or desire but is tantamount to a fact of nature.

The problem is that no facts of nature actually confer universal principles of this sort beyond the ideals that human beings themselves espouse.