Socialist Millionaires variant, where only one party learns $x=y$?
A protocol consists of parties taking turns sending messages. Therefore one party will naturally learn the output before the other (only very few exceptions exist to this rule). This means that in almost every protocol you find (especially in the semi-honest setting) you will see that either (1) the last protocol message literally is nothing more than the party-who-learned-output revealing the output to its counterpart (so you can exclude this message) or (2) the protocol is already described so that only one party gets output. In things like Wikipedia articles, it is often just simpler to describe MPC protocols as "both parties get the output", but under the hood there is generally one-sided output.

(In the Wikipedia article you reference, the protocol is written in a way that obscures the interaction pattern. The last communication between parties is in step 7 "$\langle Q_a Q_b^{-1} | \alpha,\beta\rangle$". But this step is an abstraction of Diffie-Hellman which consists of a message from each party. Just have one party omit this message and he/she will be the only one capable of learning the output.)

Protocols for private set intersection (PSI -- the generalization of socialist millionaires) are no exception. In our paper:


  Vladimir Kolesnikov, Ranjit Kumaresan, Mike Rosulek, Ni Trieu: Efficient Batched Oblivious PRF with Applications to Private Set Intersection.
  CCS 2016.


(and every other PSI paper I know of) we describe the protocol so that only one party gets output.

The building block of this protocol is something called a "private membership test" where a sender has a set $S$ of items, a receiver has an item $v$, and only the receiver learns whether $v \in S$. This sounds like exactly what you're looking for.

This private membership test building block goes back to this work (and perhaps earlier):


  Benny Pinkas, Thomas Schneider, Michael Zohner: Faster Private Set Intersection based on OT Extension. Usenix 2014.


Both of these papers are optimized to provide many instances of the private membership test building block primitive, since that is what is required for PSI. If you truly want just a single instance of private membership test, then there is probably nothing simpler than the classic Diffie-Hellman based PSI (homomorphic encryption is overkill if you just need semi-honest security). I describe it below, specialized to the case where Alice has just one item.


Alice (who has a single item $v$) picks random exponent $\alpha$ and sends $H(v)^\alpha$. Here $H$ is a random oracle.
Bob (who has a set of items $S$) picks random exponent $\beta$ and sends $(H(v)^\alpha)^\beta$ as well as $H(s)^\beta$ for every $s \in S$.
Alice can compute $(H(s)^\beta)^\alpha$ and check whether any of these values are equal to $(H(v)^\alpha)^\beta$. This will happen if and only if $v \in S$ (barring a negligibly unlikely collision in $H$).