Here is the full file of the lawsuit: http://www.ra-kotz.de/geraeusche.htm
Looks like this lawsuit was a bit more complicated. The dispute over the fridge was just one of several open issues.
This court decision has also been made by an appellate court, after the Amtsgericht had initially decided that withholding rent payments to pay the fridge with is unlawful. For some unapparent reason the appellate court finally decided that the tenant can keep the fridge money, but has to pay 9/10 of the overall cost of the lawsuit, while his landlord pays the other 1/10. Means in practice that the judge turned his fridge debt to the landlord into a judgment debt to the state. You can make your own conclusions.
There is no comparable EBK decision anywhere else, and as explicitly stated at the end of the file, this decision is not fundamental, has no legislative character whatsoever and is not binding for any other court. So no, it does not apply to Berlin. Your lawyer can bring this decision forward and the judge can take note of its existence, but that's about it.
Generally, signing a contract without having seen the renting object is not the cleverest of moves. I'm sure you wouldn't sign a rental contract over "one car". But this doesn't really matter anymore.
EBK just means the kitchen furniture is built-in or at least tries to appear built-in. There is no standardized legal definition for what it includes. Weißensee probably means East-German prefab concrete slab apartment building. In those the common EBK standard is the stove (because it needs a three-phase 400V AC connection only a certified professional is allowed to install and mess around with, because fire safety and insurance stuff) and the double bowl sink (needs a fixed water connection with similar requirements). Nothing else. Fridge can be powered from a regular wall socket, so it's your problem. Best ask your neighbors what they got when they moved in or what they have heard from other tenants. Don't put your hopes up too high, you will most likely have to buy the fridge on your own account.