I was curious, so I did a little research before bed...
From wikipedia: "Jupiter's volume is that of about 1,321 Earths"
So if you could store the full position of an atom in less than 1321 atoms then a Jupiter sized computer would work (ignore all of the other apparatus needed lets just pretend another planet is the storage medium.)
However, currently, under special conditions, the smallest we can store a single bit is in 12 atoms.
http://www.bbc.co.uk/news/technology-16543497Under more normal conditions it is theoretically more like 150-200... but let's be optimistic and go with 12... for 1 bit.
Now, if we pretend for a second that all we need is position and orientation (let's ignore for a moment the juxtaposition of the electrons and nucleus)... and if we are further optimistic that 64 bit floating point will work (64 bits of something will)... then if we go: x, y, z plus a quaternion for orientation then that's 7 64 bit values... or 448 bits.
...now each of those bits takes 12 atoms... so 5376 atoms total... per atom. For storage we would need a planet roughly 5 times the size of Jupiter.
Now, taking a step back into reality and let's go with "visible 'atoms'" that are not really molecular atoms but just "something really small to make pictures out of". Note that the rest of the world calls these "voxels" and has been using them for decades.
And this is where we get into why I believe the Euclidian tech is other a scam or so limited as to not be generally useful beyond the next Minecraft clone... I've played with LIDAR data before and it's _huge_. This is basically a 3D point cloud sampled with a laser. A street full of buildings at even 1 centimeter resolution is a pretty massive amount of data to push around. Usually it goes through a simplification process that turns it into polygons. So if the Euclidian stuff works then it must work like games like Mythruna and Minecraft in a way, where there is a larger grid that says "tree here", "elephant god statue here", and then pulls those from a highly compressed index of "tiles". You can see how repetitive the demo looks... you see the same objects repeated like a cookie cutter. This is also why non-static lighting (the stuff they said they are still working on) is likely to be impossible.
...but you know, as long as they have investors.
Note: I'd love to be proven wrong but I just don't see it happening.