。。
He'll probably choose between the two. Martial arts or death.
Literal
He [topic-は] two-option-choice [obj-を] choose [nominalizer-こと] is-probably. Martial-arts [or-か] death [or-か].
二者択一 is a 四字熟語 (four-character compound) meaning 'choice between two,' literally 'two-persons-pick-one.' The pattern X か Y か ('X or Y — which?') lists alternatives as a question to the reader, here dramatically. ~ことでしょう is a formal/literary version of ~でしょう, slightly more distancing and elegant — turning the whole preceding clause into a prediction. The short staccato second sentence supplies the stark alternatives like a drumbeat.