domgrief: Whether or not any of the above is legal in your country, or at all, remains a good question.
Some of that stuff's not even in the EULA document, but in the referenced Terms of Service.
It isn't legal in any EU country. Consumer protection rights are pretty strong in the EU and they are getting stronger with each passed legislation. Any ToS or EULAs are void the second they contradict EU law. And by void i mean VOID, no "prevelance reduction". The violating part of the EULA becomes non existand.
A general rule of thumb concerning ToS and EULAs is, that whenever a clause is so "surprising" that you won't agree to it in a normally negoiated contract, it is void.
All this Arbitrator stuff might be relevant for companies like GOG, but for the end consumer it doesn't matter. In nearly every law system that is out there, you go to court in the district the damages occured or the claimant lives.
We all are pretty damn well protected by the law. Invoking your rights is a whole different matter. For many people the pursuit of their rights is to much of a hassle to do, and many companies know that. Hell, whole businesses are build on de facto non binding contracts that the claimant simply wont pursue (think mobile ringtone subscriptions).
My experience are that huge companies usually shun the direct lights of courtrooms and unless you are going up against a central element of their business strategy(like in the Half-Life 2 case in Germany), they will try their best to pursue an out of court settlement.
All this digital selling and downloading stuff is very new, especially to something like the judical system (fun fact, most of the property laws in the western law systems are directly derived from Roman slave trade laws). Therefore there are no real precedences, but the EU is
catching up.
My advice would be to always remember that you are a customer, not an addict and Origin, Steam etc. are your contractual partners and not your pusher.