Looks like it says "may", not "shall". So the chair has the option.
Problem is that “May” is defined by an option, voice vote or show of hands.
For this vote and all subsequent votes of the entire Caucus, the Chair may conduct a voice vote or show of hands vote.
But the real crux of the story is that Trump won the vote, and then a secret ballot was requested and seconded and the chairperson approved where Cruz then won the secret ballot. I must add that a call to combine was put forth, seconded and the chairperson refused it. How convenient.
The “principled” conservatives here are, or May be, Cruzbot thieves, along with their Master.