I buy Buisman Royal Aroma Coffee enhancer from our local Dutch shop. It halves the coffee grounds needed and makes the coffee taste stronger. It is basically burnt sugar, as far as I understand.
Is it bad for you?
There are two sides to the answer. First, there is the sugar aspect. In moderation, sugar is a critical part of our diet. If you are combining it with two doughnuts and two further teaspoons of sugar in the coffee (for example) then it could potentially lead to the same insulin cycle that causes weight gain in people who eat too much sugar. The rapid intake of sugar causes your pancreas to flood your blood stream with insulin, which then drops your blood sugar lower than it should go. That causes cravings for more sugar.
The other side is how "carmelized" the sugar is. If it goes beyond a certain point, it's possible that the result could be carcinogenic, which is definitely bad.
My recommendation? Find a coffee that doesn't need "enhanced".
That site that you linked (from www.buismaningredients.com, and this one) suggest that the main ingredient is caramelised sugar. The claim is simple enough: "caramelised sugars enrich the taste of coffee" (from cited articles). Caramelisation is the thermal decomposition of sugar (sucrose); not precisely "burnt" as such but similar.
I can't find any ingredient list for that product, but the company that makes it basically produces just caramelised sugar and caramel color. I can't find any negative health claims for caramelised sugar itself other than the basic ones for regular sugar (blood-sugar effects, teeth effects, etc.). Some have concerns about caramel color.