Cross validation Deep learning

It seems to me, that above definition of k-folded cross validation algorithm (from Deep Learning book by Ian Goodfellow and Yoshua Bengio and Aaron Courville, 2016) is inconsistent with the common definition of cross - validation. In above algorithm $e$ vector is the vector of loss function calculated for every particular example in the $D$ dataset, and then mean of vector $e$ is the estimation of generalization error. Whereas in standard definition of cross - validation, we calculate test error for each fold and then calculate average of them.