@x97wehner that's actually much more complicated than I thought.
Review average is rendered using either displayRightColumnProduct or displayProductButton hooks -- what hook will be used can be selected in module settings page. It's possible to edit your product.tpl template and move one of these hooks to the appropriate place. For example, move this line.
The problem with this approach is that these hooks are shared -- many modules can, and usually do, use them to display additional information on product page. So, if you move placement of this hook within template, you will be moving content generated by other modules as well.
In other words - you can use this approach only if no other module is using this hook -- you can check in Modules > Positions. For example, in my case, if I move displayProductButtons hook it will affect Block Product Payment Logos module as well.
I will add a new dedicated hook to the module for this particular use case. That way, you will be able to call this hook anywhere in the product template, and it will not impact other modules.