Hello @Fabian,
What you showing is a jquery plugin MixitUp for filtering content. Same sort Isotop plugin.
You will need to use some custom code and there is no way to connect it with your categories fields. But you still can use it with static or dynamic items.
Here is tutorial how to use these plugins with static content: [TUTORIAL] Using Isotope and MixItUp plugins with Webflow - Webflow Tips - Forum | Webflow
And here is example of using it with dynamic items: http://forum.webflow.com/t/isotope-webflows-cms/20704
Regards,
Anna