Step 1: Understanding the Concept
A haloalkyne (alkynyl halide) is an alkyne in which the halogen is attached to an sp carbon, that is, to a carbon of the C\(\equiv\)C bond.
Step 2: Detailed Explanation
Chloroethyne is \(\text{HC}\equiv\text{C-Cl}\). The chlorine is bonded directly to a triple-bonded carbon, so it fits the definition exactly.
In the other three names the chlorine sits on a saturated sp\(^3\) carbon next to or away from the triple bond, so the halogen is not on the alkyne carbon itself.
Final Answer:
Chloroethyne has chlorine on the sp carbon itself, so it is the haloalkyne asked for. This is option (A).
\[ \boxed{\text{Chloroethyne (A)}} \]