Construct 2 is not backwards compatible with Construct Classic. We thought about it for a long time at the original launch a couple of years ago, and decided it would be better to focus on making Construct 2 as good as possible by itself, without dragging along the mistakes of Classic.
Node-Webkit is basically the standalone Google Chrome browser, allowing you to run your game as an EXE on Windows, or a Mac or Linux app. As Jase00 notes, in some cases the new HTML5 engine can outperform Classic. Further, the top feature requests we received when we were working on Classic was to support Mac, Linux and web games, since Classic only does Windows desktop, so I think C2's cross-platform abilities are a major feature and a huge improvement over what Classic can do.