Good info on strength endurance; different from "max lift" and different from cardio! Climbers and fighters need strength endurance a lot. That's largely because we are trying to get smaller muscles to do hard things, like pulling body weight, or punching hard.
But for uphill hiking, you are using mostly big muscles, like glutes and quads. The muscles themselves probably have plenty of endurance.
I think The Hikers came closest: Climbing hills is the best training for climbing hills. Most fitness is "sports specific." Even a person who is very fit in a similar sport needs to train to excel in a different sport.
But I will differ on one thing. While there is nothing wrong with the stairclimber or the inclined treadmill, they are NOT the same as going up real stairs, or going up a real hill. In "real" climbing, you are moving your center of mass uphill. You are doing Work (in the physics sense; Force X Distance). On the equipment, your center of mass is basically staying in one place. You are pushing down pedals or a belt, but it's NOT the same thing.
If you want to test this, find a building near you with at least ten flights of stairs. At a modest pace, it will take you a couple minutes to trot up those ten floors. Do 2 minutes on the stairclimber. Cool down and recover, and then go trot up the ten floors. You will notice a DRASTIC difference in the amount of work.
I don't know where you live, or what "uphill" resources you have near you. If you have a tall building with stairs, or a decently long and steep hill on a road, get out of the gym and go train on that. You can design all sorts of workouts depending on the length of the hill or stairs. Do reps, vary paces, "fartlek" (speed play), carry weight, etc.. For weight, I recommend water in gallon plastic jugs in an old pack. It's nice and heavy, and it won't hurt you (I've carried rocks, but you end up with bruises). Also, you can drink the water at the top. And, most importantly, you can pour it out at the top, so you don't endanger your knees carrying the weight back downhill.
Good luck! (And you do look skinny...)
TCD