We investigate video classification via a two-stream convolutional neural network (CNN) design that directly ingests information extracted from compressed video bitstreams. Our approach begins with the observation that all modern video codecs divide the input frames into macroblocks (MBs). We demonstrate that selective access to MB motion vector (MV) information within compressed video bitstreams can also provide for selective, motion-adaptive, MB pixel decoding (a.k.a., MB texture decoding). This in turn allows for the derivation of spatio-temporal video activity regions at extremely high speed in comparison to conventional full-frame decoding followed by optical flow estimation. In order to evaluate the accuracy of a video classification framework based on such activity data, we independently train two CNN architectures on MB texture and MV correspondences and then fuse their scores to derive the final classification of each test video. Evaluation on two standard datasets shows that the proposed approach is competitive to the best two-stream video classification approaches found in the literature. At the same time: (i) a CPU-based realization of our MV extraction is over 977 times faster than GPU-based optical flow methods; (ii) selective decoding is up to 12 times faster than full-frame decoding; (iii) our proposed spatial and temporal CNNs perform inference at 5 to 49 times lower cloud computing cost than the fastest methods from the literature.