This is wrestling not "push hand". Different style of Tai Chi they have slightly different push hand method. Chen's is very different (they have grappling, locking, catching...)but is not this. In the history of Tai Chi teaching and training, wrestling training method was first merge into the system in Beijing (mid to last 19th century). Today, the Wu (吳) Tai Chi in Hong Kong still have wrestling training but they won't say this is "push hand". The famous masters Wu Tai Kwan, Cheng Tin Hung, Wu Sing were all good in wrestling technique. The wrestling technique has proven as a very useful technique in both street fighing and in martial art competition. In my personal point of view include wrestling training in Tai Chi's system is a positive direction.
I saw some articles claimed that Chen village did employ some wrestling instructors (in 1980's) to train and pass wrestling technique to Chen's villager (student). I think it is a positive development, but also I think we should know the real history.