Clumsy, and grammatically incorrect.
There is an aberration taking strong hold in America, where the Present Perfect and Past Perfect tenses are now formed as:

has/had + Simple Past Tense !!!
"...but I had went to the movies."

You are right. Those tenses are formed:
has/had + Past Participle.
'club' can be regarded as singular or plural. I presume the writer regards 'waiting' as referring to the individual members, and so, regards it as plural.

It is the closest the club have come to ending their wait.

Thank you Gervais for the reply.
I think if I were (past subjunctive) to teach this I would correct it to the simple past by removing the incorrect auxiliary "have".
So: It is the closest the club came to ending their wait.
Thanks again for your reply.
Uncle Gary.