Can I make Turkish Delight with jelly powder? I have come across some Turkish Delight recipes calling for cornstarch, others for gelatin, some use both and one that uses store-bought jelly powder (aka gelatin dessert aka Jell-O).

The jelly powder recipe confused me because it has few other ingredients, so how does it end up with the texture of Turkish Delight rather than gelatin dessert?

On the other hand, using store-bought powder gives me easy access to lots of flavours. Can I use store-bought jelly powder to make feels-like-the-real-thing Turkish Delight?
As the answer to the linked question states, original Turkish delight is made using only cornstarch. 
I understand you're asking specifically about the recipe linked and how it differs from other recipes. I'll try to answer the following points:

Q: Why do some recipes call other gelling agents such as gelatin, next to cornstarch.

A: Like most thickeners, gelling agents, cornstarch is also susceptible to syneresis/weeping. Using other hydrocolloids helps preventing this. In Turkey, apart from traditional confectioneries, to cut down the syneresis, pectin is mainly used as the choice of additional gelling agent.

Q: Can gelatin alone be used to get the same texture, as the traditional Turkish Delight?

A: The answer is simply: "No". As gelatin will form a brittle gel, which is not really even close to texture of the gel that would be formed by gelatinized cornstarch.