This is a very basic strike/counter combination in the Fu taiji system. You see it there because Fu taiji developed out of bagua, via Fu Zhensong, who was reputed to be the only internal master who could rival Yang Chengfu at push hands. (They were great friends:)
Fu's son, Fu Wing Fay, a contemporary of Cheng Man-ch'ing, specialized in taiji and leungyi, which is a hybrid taichi/bagua forms. This is likely why you see this elbow strike/counter in Fu taiji.
The counter is simple, but it requires bagua coiling hands.
- Use the forearm for pushing
Hand and wrist must be free. Ideally, you maintain contact forearm to forearm, because if you let your partner contact closer to their wrist, they will be able to get a little more distance in that elbow strike before you counter.
- When the elbow comes, coil the fingers downward around the back of the elbow
This would be right arm to right arm, or left to left.
- Turn the waist outward and empty
Outward refers to the side of the hand being used. If right hand, waist turns right. You need to be able to empty the chest in conjunction with the counter, to get sufficient leverage against a skilled partner, and the feeling should be that the movement here derives from the base of the spine.
- If the opponent's body is turned by the counter, continue coiling the countering hand under their arm until your fingers can grasp the partner's throat.
Be gentle! This is not a brute force application! Anyone can squeeze the trachea, but can you apply and maintain this with only the minimum required pressure?
The off-hand controls the base of their spine.
Using this hold, you can gently keep the partner at the edge of imbalance indefinitely, such that they cannot strike or employ their body in any useful way. It requires some feeling, b/c then the partner tries to move, you must adjust to keep them from achieving any root.
- The counter to the counter is to roll out
Direction of the roll is the same direction the partners body moved when they were turned around. I use "roll" here because, while it can look like a bagua spin-turn, it's really more of a body turnover.
(Spin turn is difficult/impossible when you have no root, but body roll is natural from the edge of balance, of when off balance, and this is a basic principle of bagua.)
When the counter and the counter-counter are employed correctly, the players return naturally to push hands, with no break in continuity.
- I think the reason it's considered optimal in the Fu system is it establishes superior leverage from from the beginning of the strike, not waiting for it to develop, but deflecting and and using the force of the opponents body to turn it and step behind to grapple, controlling the neck and spine.
It's elegant and it works. Caveat is that Fu system teaches a core curriculum of taiji/bagua/hsingyi where possible, so it may be difficult to use without that base.