Is it really all that hard to have a demo site for these things? It would be a lot of fun to play with crossing pictures. I'm guessing it's because using a graphics card in the browser isn't good enough yet?
I'm not sure how fast their FastPhotoStyle approach is, but a TensorFlow implementation of the original neural style transfer can take upwards of 20 minutes to create the final stylized image. If someone had the pre-trained model and neural net code in JS to read it and you could do it all client side then it would be possible, but still very slow.
The tech has come a long long way since the original, even before this FastPhotoStyle project.
A few months ago, there was TensorFire [0] that was able to do it in the browser. Quick google also gives other results [1]. There's also many apps that can do it in seconds. Speed definitely isn't an issue anymore, but getting it to work in browser can be tricky.