How to make my user notifications module notify node authors about new comments?
As per the "Or is there another way to make this work without the custom module I'm struggling with?" in your question, IMO the answer is yes. Read on for more details about how to "send a notification to the article owner when some user comments on the review added to an article." (as in your question).

Have a look at this, rather basic, rule (in Rules export format):

{ "rules_notify_node_author_about_new_comment" : {
    "LABEL" : "Notify node author about new comment",
    "PLUGIN" : "reaction rule",
    "ACTIVE" : false,
    "OWNER" : "rules",
    "REQUIRES" : [ "rules", "comment" ],
    "ON" : { "comment_insert" : [] },
    "IF" : [
      { "NOT data_is" : { "data" : [ "comment:node:author" ], "value" : [ "comment:author" ] } }
    ],
    "DO" : [
      { "mail" : {
          "to" : [ "comment:node:author:mail" ],
          "subject" : "A new comment was posted to the node you authored",
          "message" : "A new comment was posted, you can find it at [comment:url]",
          "language" : [ "" ]
        }
      }
    ]
  }
}


Use the Rule UI to import it in your own environment. Some more details about this rule:


Event: After saving a new comment.
Condition: Check that the user who posted the comment is different from the node author (I'd think it doesn't make sense to notify the node author of comments posted by the node author, right?).
Action: Send an eMail to the node author, with a link to the comment that got posted.


Feel free to add any rules conditions that may fit to further improve the above prototype, to fit your actual requirements.

Note that the above rule doesn't depend on any other module, though you could make it way more sophisticated if you'd also get the Message module involved (eg to create a log file of all such eMails ever being produced, if that's what you'd want to do).

BTW: no need for custom code ...