For this pushup, instead doing pushup on the ground, it's done by placing your feet & hands on chairs - both feet on a chair & a chair for each hand. This pushup allows you to go deeper but I am concerned about the effect on shoulders/chest & any muscles related.
On my Thursday cardio day, I do push-ups with an exercise ball (Monday is my chest day) which is a warm-up for my core exercises. The shoulders/chest will be affected but I'm not too concerned about it because my chest likes it and my shoulders do not seem to be affected for the Friday legs/shoulder workout. For me, this type of push-up seems easier on the chest and shoulders but the core stabilization is definitely a challenge when you are placing your ankles on the ball - much easier if the knees are on the ball.