Touch is an important channel for human-robot interaction, while it is challenging for robots to recognize human touch accurately and make appropriate responses. In this paper, we design and implement a set of large-format distributed flexible pressure sensors on a robot dog to enable natural human-robot tactile interaction. Through a heuristic study, we sorted out 81 tactile gestures commonly used when humans interact with real dogs and 44 dog reactions. A gesture classification algorithm based on ResNet is proposed to recognize these 81 human gestures, and the classification accuracy reaches 98.7%. In addition, an action prediction algorithm based on Transformer is proposed to predict dog actions from human gestures, reaching a 1-gram BLEU score of 0.87. Finally, we compare the tactile interaction with the voice interaction during a freedom human-robot-dog interactive playing study. The results show that tactile interaction plays a more significant role in alleviating user anxiety, stimulating user excitement and improving the acceptability of robot dogs.