Do the seated outer thigh machines actually work?

Yes, the seated outer thigh machines do work; however, not for the muscles or the reasons that most people are trying to target.  Most individuals use the outer thigh machines to try and target the outer hip muscles in an attempt to burn fat on the outer hip region.  This thought process plays into a myth known as "spot-reduction" which is centered around the idea that performing exercises for specific muscles will burn body fat in the same area.  While exercises for the outer hip muscles may help make them stronger they will not help make you leaner in the hips.  To get rid of the fat around the hips, focus on proper nutrition and participating in a structured exercise program consisting of resistance and cardiorespiratory training.  Doing so will decrease fat stores throughout the entire body, including the problem areas.  Also, the seated position in which this exercise is being performed changes what muscles are primarily doing the work, turning what most people think is a glute exercise into one that challenges other muscles called the piriformis and tensor fascia latae (TFL) muscles.  The significance of this is that both the piriformis and TFL when overactive/overworked will actually decrease the activity of your glute muscles!  Additionally, while the piriformis and TFL perform similar functions to the glutes, they are much smaller and when overworked can contribute to a number of movement problems and injuries.  One of many great alternative exercises to the seated outer thigh machine that actually targets the glutes is the side-lying leg raise.  Begin performing the side-lying leg raise by lying on one side of the body with your back slightly away from a wall; bend the bottom knee up toward your stomach and keep the top leg straight.  Draw-in your belly button to tighten the abs and while pressing the heel of the top foot against the wall, slowly raise top leg up sideways 30-45 degrees, keeping the knee straight and toes pointing slightly upward.  Pause at the top for 2 seconds and slowly lower your leg back to the start.  Perform 10-15 repetitions for each side.