As somebody who works in a technical support/development position, the fact that you people are expecting compatibility from a public beta of an operating system with a live application is ludicrous.
This is not a full operating system. It is a technical preview, it is not a complete build of what is going to be released as the actual product.
Why would Riot be concentrating on making sure their application runs on a technical preview? Applications and Operating Systems change when going from Beta to Beta to official release.
Its not like pulling a lever the game is automatically compatible with the operating system. It takes time to write the code in development, work through Q&A and then finally get pushed out to the actual product.
You take a risk when you decide to install a beta of an operating system. There are no guarantees it will work with any existing application that doesn't belong to Microsoft and even when the official build of Windows 10 releases, it does not mean LoL will even be supported with it then.
Companies never jump on an operating system when it first releases, doesn't anybody remember Windows Vista? We have products within my company that are just getting supported with Windows 8 and we provide hospitality management software for properties around the world.
Obviously not everybody with a technical background knows or even understands this, but what you're asking for is just absurd. If LoL doesn't work with this new patch, revert to your previous operating system. Riot has no obligation to ensure their product works with a technical preview of an operating system.