In his 1963 introduction to Suicide of a Nation?, Koestler says that he coined the word and I think we have no reason to doubt him. Note that on its first appearance the word was misprinted!
A chimaera, in Greek mythology, was a monster with a lion’s head, a goat’s trunk, and a serpent’s tail; more generally it meant a composite animal. Throughout the ages, painters and writers of fantastic tales have been fond of creating chimaeras. My own favourite brain-child is the momiphant. He is a phenomenon most of us have met in life: a hybrid who combines the delicate frailness of the mimosa, crumbling at a touch when his own feelings are hurt, with the thick-skinned robustness of the elephant trampling over the feelings of others. I think the sizeable majority of Germans of the last generation who supported the Fuehrer belonged to the species of mimophants. They were capable of shedding genuine tears at the death of their pet canaries; what they did at other times is perhaps better forgotten.
Arthur Koestler, ed. (1963). Suicide of a Nation?, p. 7. London: Hutchinson.
In a 1972 essay, Koestler did use the word to describe Bobby Fischer, but this was a decade after he had first used the word in print:
But what kind of secret personality is hidden inside Bobby the Tartar? Spassky said he was suffering from persecution mania; others that he had megalomania; that he had never grown out of being a boy-wonder; or that he was just simply mad as all geniuses are supposed to be. I gladly agree that there is some truth in all these explanations, but I prefer my own, which is simpler; Bobby is a mimophant. A mimophant is a hybrid species; a cross between a mimosa and an elephant. A member of this species is sensitive like a mimosa where his own feelings are concerned and thick-skinned like an elephant trampling over the feelings of others. All of us have met individuals of mimophantic dispositions, but Bobby is the perfect representative of the species. His vulnerability is genuine. The cameras do upset him. He cannot bear street noises. The chair on which he sits while playing, the size of the board grate on his mimosaeque† sensitivities. At the same time his elephantine skin prevents him from realizing what he does to others. ‘I like to see them squirm,’ he commented on his opponents. ‘I can see their ego crumbling.’ And his favourite comments on his own moves are ‘a smash’, ‘a crunch’, ‘a chop’.
Arthur Koestler (1972). ‘The Glorious and Bloody Game’. In The Sunday Times, 2 July 1972. In The Heel of Achilles: Essays 1968–1973, pp. 207–208. London: Hutchinson.
† Sic. Koestler seems to have been unlucky with the proof-readers at Hutchinson.
Several writers familiar with Koestler (1972), but not with Koestler (1963), seem to have assumed, probably independently, that he coined the word specifically to describe Fischer. A couple of examples:
[Koestler] was intrigued by Fischer’s personality, so tough and yet so sensitive, and he came up with another hybrid, the mimophant, mingling the touchiness of the delicate mimosa plant with the toughness of the thick-skinned beast.
Melvin J. Lasky (1983). ‘Remembering’. Encounter 61, p. 63.
In Reykjavik to cover the match, the novelist Arthur Koestler famously coined the neologism “mimophant” to describe Fischer.
David Edmonds & John Eidinow (2004). Bobby Fischer Goes to War, p. 24. New York: Ecco.