I think you're correct that the definition of what is "left" and "right" doesn't really account for the current political climate. This is why I think the parties are due to realign, at least in the U.S.

It's also worth noting that up until now, the American right has focused on limiting the influence of the national government. In contrast, the right wing in Europe has few issues with big national governments. The extreme right in Europe might even want to reintroduce their respective monarchies. That is to say the word "right wing" doesn't mean the same thing everywhere. However, Donald Trump seems more in the vein of a European right-winger, which new and surprising in U.S. politics.