The version in the paper only is ever multiplying by 1 or -1, so you do not need a full multiplier circuit. The weights are also stored as signed integers, not floats, so no complicated floating point circuity. I am not sure what current state of the art is, but considering the cost of multipliers/floating point circuity I would be surprised if it changed to those if signed integers work.

All branch predictors need some way of storing their state and selection logic, and the way a perceptron branch predictor stores its data is just a big table indexed by some hash of the program counter of the branch, which is pretty standard for branch predictors. Also, all branch predictors have a sort of "backpropogation" in that pipelined processors produce the actual result of the branch (possibly many) cycles later, so this also is not as much of a factor. Since the training is a function of the weights you do not need to store extra data beyond the threshold, but that is already being computed as the prediction anyways.