How HOTP values are validated according to RFC 4226
I agree that Gilles' interpretation in the comments is the only one that makes sense; the RFC clearly contains an editorial error, and should read either (emphasis indicates corrections):


  "If the value calculated by the authentication server matches the value calculated by the client, then the HOTP value is validated."


or:


  "If the value received by the authentication server matches the value calculated by the server, then the HOTP value is validated."


The first sentence in your quote isn't grammatical anyway: the words "HOTP client" appear to have been randomly and meaninglessly appended to it, perhaps as a result of careless copy-pasting.

The IETF has a whole bunch of errata for RFC 4226, but this particular mistake doesn't appear to be listed there.  You might want to report it yourself.