Mixing starches with sugar to make chewy candies
I think it'll be very difficult to mix everything without any liquid, but if you cook everything long enough until (almost?) all liquid is evaporated, maybe it's not necessary to list it anymore. 

But here is some info to get you started on your experiments:

In Germany there are tons of "vegan gums" with very similar ingredients like your candy, but they all list fruit juice. 
I found a product with slightly more detailed ingredients list than usual that may be similar to what you ate here. If you experiment with the added liquid, you may get chewy candy. 

The shortened and generalized list of ingredients is:
invert sugar syrup; 15% fruit juice; starch, glucose syrup, 4% ginger pulp; acidifier; ginger extract.

Usually, "starch" refers to potato or corn starch here. But I've seen "modified starch" on the packages and "tapioca starch", too.

Unfortunately I only found one recipe to cook something similar to that here (also in German, sorry). The ingredients if condensed are also basically sugar, starch, liquid, some carrageen (see note #1) and flavouring. 

The tl;dr recipe would be: 


Mix everything, bring to boil
Stir a lot until the bottom of the pan becomes visible between strokes
Dial down and continue cooking while continuously stirring until "your desired toughness" is reached. To test this, a small piece is dropped into cold water (sounds a lot like cooking sugar). 
While warm, the mass can be pressed into molds (either starch dusted or silicon). The oil is used to remove the starch and bring it to shine.


Annotation #1: The mentioned recipe uses "Tortenguss" which is mainly modified starch and some carrageen. Also, the author uses three types of sugar (refined sugar, glucose and fructose).

Annotation #2: Someone in the comments of the mentioned recipe reported that they cooked everything so long it became hard candy.