Reaction of 1 equivalent of Mg in ether with 1,4-dibromobut-2-yne
Cyclobutyne cannot exist.  There is no way to enforce 90° bends at both ends of a triple bond, but the carbanion formed by the Grignard reagent synthesis finds an easy way around this problem.

Let's say the magnesium reacts at position 1.  Then the negative charge would couple with the conjugated triple bond to spread to position 3:

$\ce{Br\overset{+}{Mg}\overset{-}{C}H2-C#C-CH2Br &lt;-&gt; Br\overset{+}{Mg}CH2=C=\overset{-}{C}-CH2Br}$

Then the carbon atom at position 3 can act as a nucleophile, displacing the remaining bromine as a bromide ion to give the product named in the book.