I did recently read an article about remapping or chipping a car and it is possible to achieve better MPG at the same time as also getting better performance however if I was getting it done then i'd be getting a garage to install it rather than buying this shit.
Reading the advert all the clues are there about it being a scam especially regarding how much fuel saving you can / will make -
They refer to cutting your fuel consumption in half however they also state you can save 35 cents in the dollar on fuel so that's errr only 35% not 50% and the information on the box says 15%
So which is it

Anything that claims both a power increase and fuel saving without a remap is best avoided, what you have read is true, a professional remap does increase power, and not using all that power can increase mpg, the engine burns fuel better than at factory settings .
When buying a car you are often given a choice of power levels for which you pay more or less, it is a factory remap of the same engine, or a different ECU.
With my previous Golf I had the highest option, but found out the lowest option can be remapped to a higher output than the one I bought could be remapped to, same thing with some BMW models apparently.
My guess is they do not expect the lower power ones to be remapped, but do the higher power, and put restrictions within the ECU.