It's kinda funny the whole 'new game' thing. It's not a new game in the sense that it's been redeveloped with new code, like C# for instance. Same game, same core game code. VEM is a part of that, as is any other software they used.
Why the graphics 'look better' is actually simple.
Flash as framework and delivery system was never designed to handle raster images, in fact going back to the beginning when it was a plugin for Director, where I first started using it, the issue of compression was there from day one. Flash simply sucks in that regard, it is after all a vector graphic development platform for animation.
With porting the game into Unity, the game at least now has the advantage of being able to utilize the capabilities of processing raster images properly, well a whole lot better anyway, much much better. Mainly the compression algorithms used are designed for jpg work. If I remember correctly, Unity is also capable of processing RAW formats as well which if true, would allow it to push out HD quality static images at the expense of resources.
The images in the game were shot at pretty high resolutions, high for what it was back 10 years ago. Those images are already in a processed state within the game, but now that the game is using Unity for encapsulation and delivery etc etc, the images have a bit more punched up appearance and feel to them. Not a huge amount, but some. If you crop and view at 100%, the images are still blown out, look almost like they do in Flash, you can't get away from that completely.
Other graphic elements within the game will look nicer again because of Unity, and how it outputs. The avatars will only really look as good as they were designed. If they're low poly coming in, they're going to look it going out.
The other reason the 'graphics' can appear to be 'better' is that the game is utilizing video codecs and drivers much better thanks to Unity. It is still using a browser framework, but not as an application. If you have a decent video card and monitor the game can and will look a whole lot nicer. If you use the software that came with your video card to tweak the visual appearance of the game, it can look pretty nice actually. It's not going to affect how the game plays, VEM still going to throw your ball into the weeds now and then but at least as it sails away it'll look nice doing so.