After upgrading the BI Connector to 2.2.0-rc1, I followed these instructions to connect using Tableau. With the help of adinoyi.omuya, I was able to sort it out. There were a few problems:

1. I did not have the MySQL client installed. Since the documentation didn't state this as a step, I assumed I wouldn't need it. Installing MySQL was one of the steps I executed to resolve the issue, although adinoyi.omuya has since told me that it shouldn't have been necessary.
2. After installing the MySQL client, it was necessary to move the plugin file to the directory pointed to by mysql_config --plugindir (as documented here, rather than the location specified on the other docs page (/usr/local/mysql/lib/plugin/).
3. I have a version of Tableau that predates the link to MongoDB. It was necessary to use a modified version of the .tdc file that replaced mongodb with mysql.
4. I had another .tdc file, which I renamed in order to ensure that Tableau would read the correct file.
5. After modifying the .tdc file, it was necessary to restart Tableau. This is mentioned in a different section of the docs page, but not the section I was following.

After performing these additional actions, I was able to connect using the plugin. It's unclear to me whether all of the steps above were necessary; as noted, it may not be necessary to have MySQL installed, which would presumably mean the plugin file can be located at the path quoted in the docs. However, it seems clear that the .tdc file contents need to be correct, and Tableau should be restarted if it's open while the .tdc file contents are modified.