Is this an it-cleft with bare infinitive?

Question

   "Actually, we didn't get lost," the tall one says. "We ran away."
   "Not running away so much as just stumbling onto this spot and deciding to stay put," the brawny one adds. "That's different from getting lost."
   "Not just anybody can find this place," the tall soldier says. "But we did, and now you have too. It was a stroke of luck--for us, at least."
   "If we hadn't found this spot, they would've shipped us overseas," the brawny one ex-plains. "Over there it was kill or be killed. That wasn't for us. I'm a farmer, originally, and my buddy here just graduated from college. Neither one of us wants to kill anybody. And being killed's even worse. Kind of obvious, I'd say."
   "How 'bout you?" the tall one asks me. "Would you like to kill anybody, or be killed?"
(Kafka on the Shore, tr. by Philip Gabriel)

Why does the first phrase have bare infinitive? (If the first be an it-cleft, CGEL says the type is normally inadmissible (p.1422), and Bas Aarts also says in his book to infinitives are allowable not in it-cleft but only in pseudo-cleft.)

Answer 1

The first phrase is not an it-cleft, which is clear from the complete lack of a subordinating clause. An it-cleft is it + be + X[usually NP] + subordinate clause

it + was + the fall from the cliff + that killed him

Note that an it-cleft does not have a to-infinitive.

kill or be killed is an idiomatic phrase, a single lexical unit sometimes called a Siamese Twin, that describes a situation. The first phrase is actually a simple declarative sentence "It was X" describing a situation or state.

It was crowded

It was dangerous

It was noisy

It was do or die

It was kill or be killed

The second phrase is part of a question, asking "Would you like to X?" As it is asking about a like, it has a to-infinitive.

Would you like to eat?

Would you like to sleep?

Would you like to kill?

To-infinitives are commonly used when talking about thoughts or feelings:

He chose/wanted/decided/liked/hated/expected/hoped/etc to shoot his enemy

Answer 2

“Kill or be killed” is a set phrase and could easily be set off with quotes or italicised in that passage.

Dictionarist.com has:

kill or be killed
one must protect oneself, it is preferable to kill someone instead of allowing them to kill you

The brawny one explained that over there, they either had to kill someone or be killed themselves.

Grammatically, although kill is uninflected in the set phrase it’s probably better parsed as imperative than infinitive.

An “it-cleft” sentence starts with it and presents two pieces of information which could be presented in a single clause.

It was her mother who did the washing
Her mother did the washing

“It was ‘kill or be killed’” is not such a construction.