Hi Lukas,
The Mendix-server is running on Java so you need JRE always. Read the installation manual.
To run the Mendix application from the browser no Java is needed. That works with html and javascript.
The model that you create is "run" by the Mendix runtime. This runtime is written in java (you might have noticed a bunch of .jar files in your Program Files/Mendix directory). So, to run a model locally, you will need a JRE.