Yeah, I'm not surprised that a transpiler produced code that was faster than handwritten code. For a lot of games, I'd guess you're right and the GPU is the bottleneck. Anything that heavily taxes the CPU however (lots of physical entities, and/or graphics techniques that require per-frame CPU use I would expect to suffer pretty heavily.
WASM is still running in the JS VM. No matter what you do, you're still going to pay that price, and running a JVM inside a JS VM is likely to be a pretty hefty cost for CPU intensive games. A better bet longterm is to wait for WASM to support garbage collection, at which point transpiling Java source to WASM code will be a more viable option. Porting the rendering pipeline to WebGL will still probably be tough (WebGL still has some rough spots), or at very least a big job. Also, I think a lot of shaders will need a rewrite for WebGL. I'm not sure of the specifics, but as I recall WebGL shaders aren't 100% compatible with any of the stock GLSL versions.
With a WebGL rendering backend and WebGL compatible shaders, for now transpiling with something like JSweet would probably at least produce a functional result. As I remember, one of our forum members was working on just that a few months back. Haven't heard any news on how far he got with that though.
I don't think the biggest problem with porting to the web is language support or VM performance. The biggest problem is that JS and web tech are, by design, heavily restricted and a very, very different platform from the JVM. Things Java developers take for granted, like using background threads for disk I/O or raw network access, are either totally missing or exist only in heavily restricted and modified forms (I.e. WebWorkers and WebSockets) that often have an unstable API or differing levels of support on different browsers. Stability and support is improving for web tech, but it still has a TON of gotchas for native/JVM developers that cause all kinds of headaches. It's better if you're deploying to something like Electron where you only have one version of Chrome to support, but Electron is hardly a silver bullet and it has all its own headaches. It would be nice if there was a way to deploy jME games for the web, but I'd question the sanity of a monkey deploying a game to Electron instead of a desktop VM/proper mobile builds.