Minis, themselves may not be required, but just looking at the sample characters, you need some sort of grid system, and markers/tokens/whatever to represent creatures and PCs. There is way to much pushing/shifting/teleporting/whatever going on at low level to toss it back into the abstract, which is unfortunate. Flanking, opportunity attacks, reach, all these seem multiplied in 4e, and a lot of monster abilities seem to depend on being adjacent or shifting to or away from something.