They are, and the interconnects are 4 bit. These were used by first year undergraduates for years before the Big Hex Machine was built, so sturdy Ethernet cables were cheaper and more reliable than many other options.
Yup, we used 4 wires for data and 4 for power - there's a 12V supply which is spread around and downregulated to 5V on each board. We picked ethernet because it's extremely cheap, hard-wearing, widely available and has enough wires to play with.
A 4 bit differential output would be pretty darn good.
Actually, that might be the case: some boards have 4 presumably output ethernet ports.
edit: https://bighexmachine.github.io/hexModuleSpec/ looks like I'm right?