In the context in the post, I’m saying that before we get rid of an assumption of probabilities, it is easier to first get rid of the assumption that we have a real-valued L (proving it from other assumptions instead). We do this by applying VNM, still assuming mixed strategies are described by probabilities. I finally get rid of that assumption a few paragraphs later. I edited the post a little to try and clarify.
In the context in the post, I’m saying that before we get rid of an assumption of probabilities, it is easier to first get rid of the assumption that we have a real-valued L (proving it from other assumptions instead). We do this by applying VNM, still assuming mixed strategies are described by probabilities. I finally get rid of that assumption a few paragraphs later. I edited the post a little to try and clarify.