Hmm, this is a little confusing. Let me explain.
"mysql" and "mysqli" are two PHP extensions which can be used to connect to a MySQL server. We have both of them installed on all versions of PHP that we currently provide, so which one an application uses is up to the way it's designed (and/or configured).
With that in mind, you should already be able to use the "mysqli" extension to connect to a DreamHost MySQL server. There's no extra setup needed.