Ring dips and toes to bar are two gymnastics movements found in many workouts that pack a whole lot of bang for the buck. Put them together and you have a nasty little workout.
Many clients remark how sore they get in their chest from both movements. Ring dips seem more obvious, given the upper body horizontal pushing demands. Toes to bar produce more confusion as to muscle soreness in the chest. The prime mover in the toes to bar would seem to be the anterior core muscles (rectus abdominus, psoas, illiacus) and no doubt my gut is a bit sore for a day or two after lots of toes to bar. Given the hanging state of the athlete the upper body is naturally involved. While it is apparent that the shoulders go through flexion and extension, less obvious is the amount of shoulder adduction. As the pec major is the prime shoulder adductor, this explains why the chest is a bit beat up after high rep toes to bar. This also explains why it can be incredibly difficult to transition from ring dips to toes to bar in a metcon.
If this combo shows up in the Open, make sure you include a good aerobic prep with movements low in eccentric demand but that still get some good blood flowing to those specific areas. Burpees and mountain climbers would be great choices for general aerobic prep. Follow that up with a few rounds of the actual movements themselves, keeping the rep scheme low as you are simple getting the nerves prepped to fire correctly.