I put the slopes really close to each other to the point where even though there's a little hole, the Lemmings will walk up the slopes instead of walking down back to the place it came from. Seems like a normal thing to me.
It's hard to tell what you mean since I don't have PSP, but in any case I really wouldn't call it the same thing since it's about walking not climbing. The behavior you see here with the climber in DOS Lemmings only happens because for some reason, the game shifts the climber an additional pixel away from the wall when it bumps its head and falls. In other words, instead of landing at exactly where he was before he starts climbing, he lands even farther away from the wall than he was located the last time he's still walking.
Another way to see the strangeness of it is, if the terrain was more like this
XXXX
...X
...X
...X
...X
...X
...X
...X
...X
...X
X.YX
Starting from Y and after climbing up the wall on the right, he would fall straight through the X.Y gap rather than landing on Y, even though in both this case and in your level, you have exactly one pixel of terrain and one pixel of gap.
It's hard to find a logical way to explain for that additional distance shifting away from the wall. In DOS Lemmings walkers will always fall off even a one-pixel gap. In PSP with higher graphics resolution, it may be possible to create terrain that have tiny gaps narrower than the distance a lemming moves walking a single step, but I would think that when the gap is wider than the single-step walk distance a walking lemming would probably fall too?
In any case, I have to say glitch or not, even the original levels from the game seem to have more interesting examples of builderless level ideas than the one you present. You may want to create a few more other examples featuring other ideas and then maybe put them together in one level.