This exercise is hands down one of the BEST GLUTE BURNERS you will ever feel (if it's done right)!! Just like the glute med wall lean, this exercise is an ISOMETRIC HOLD. I have found (similar to Dr. Powers' Hip Progressions) that isometrics are CLUTCH for getting people to activate and feel their muscles working. The BIG KEY with this exercise is that the stable hip (the left leg here) DOES NOT MOVE. Root yourself into the table, and keep that leg completely still. The position is a tad bit of knee flexion and a little more hip flexion (think of a SL squat with nice forward trunk lean).
Place your other leg on the moving reformer part. USE A LIGHT RESISTANCE FIRST. Kick out the sliding part with this leg. The key is that while you are kicking, your stable leg/hip DOESN'T MOVE AT ALL. Remember: isometric hold. Kick slowly out and in, and really control not just the kicking leg, but your whole body. If your stable hip is moving, you won't feel it at all. It's all about controlling the increased demand as you kick out. As they say in FRC, irritate tension through the whole body while doing this exercise.
I was taught this exercise by my former CI Brandan and stud clinical team at Kaiser West LA. They have opened my eyes to all the amazing uses of a reformer. We used this particular drill in a patient 5months post-op ACL who had an extremely difficult time recruiting her glutes. What was interesting is that her form on all of her movements - squat, deadlift, plyos - all looked fantanstic. But she NEVER felt it in her glutes. Even changing her movement to biomechanically bias the glutes as much as possible did nothing. Other isometrics - nothing. So we used this exercise to "wake them up" and allow her to get that mind-body connection on what it feels like to fire her glutes. We then transitioned back to our compound lifts and wha-la, she was finally feeling her glutes!