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It wasn't as strange as it might seem for the author to coin OK as an abbreviation for "all correct." There was a fashion then for playful abbreviations like i.s.b.d (it shall be done), r.t.b.s (remains to be seen), and s.p. (small potatoes). They were the early ancestors of OMG, LOL, and tl;dr. A twist on the trend was to base the abbreviations on alternate spellings or misspellings, so "no go" was k.g. (know go) and "all right" was o.w. (oll write). So it wasn't so surprising for someone come up with o.k. for oll korrect. What is surprising is that it ended up sticking around for so long while the other abbreviations faded away.