The usage in question uses any longer right before a finite verb instead of at the end of the entire sentence:
Now I can’t see that crisis any longer means a climax, unless we are willing to grant that every breath of wind has a climax (which I am) (...)
That is saying that for the writer, a crisis no longer means a climax as it perhaps once may have. It doesn’t mean that anymore. Or simply that it does not still mean that. So one simple way to look at the meaning of this use of any longer is by swapping it for the adverb still:
Now I can’t see that crisis still means a climax, unless we are willing to grant that every breath of wind has a climax (which I am) (...)
That has the same meaning as the original.
The OED describes this sense under its section on the idiomatic phrases of the adverb long in this (paywalled) way:
P3. Idiomatic phrases.
- d. no (also not any) longer: not from the point specified or implied, in contrast with the situation at an earlier time; (also, in stronger sense) never again. Cf. sense 2b, and no more adv. 1a, 1b.
They provide examples from the past two centuries that include these, where I’ve added bold to make it easier to see the demonstrated use:
- 1841 T. Carlyle On Heroes vi. 327
Nature..was as if effete now; could not any longer produce Great Men.
- 1894 H. Caine Manxman ɪɪɪ. xix. 190
There was no longer any room for doubt.
- 1959 Life 8 June 156/2
He admitted that once there had been some [slave labor camps] but not any longer.
- 2005 Computer Buyer May (Compl. Guide to Media Center Suppl.) 20/3
One of today’s hot topics among future-gazers is whether TV programmes will no longer be broadcast over the airwaves.
The sense 2b which they reference there is this:
- b. In comparative, chiefly with adverbs or adverbial phrases indicating degree, as any, no, much, a little, etc.: after the specified or implied point in time.
That’s probably more like what you’re used to seeing. It’s a sense closely related to the one that puzzled you.
This one is just like no longer but becomes any longer under negative concord.
They provide citations for it like:
- 1975 B. Donoughue Diary 25 June in Downing St. Diary (2005) xvii. 431
It is clear that this Prime Minister should not go on much longer.
- 2011 T. Wakefield Knuckler ix. 155
The 2003 Red Sox had too much at stake for the experiment to continue any longer.
Your example used any because it was in a negative context, governed by can’t see. Outside negative contexts that therefore require any for negative concord, you would instead use no longer directly:
- I do not plan to stay any longer than my wife does.
- I plan to stay no longer than my wife does.