It is certainly gamed, but maybe not in the way you mean it.
The fundamental issue is that every agent in the economy has their own price index, condensing this into a single number is impossible without losing almost all the information.
Essentially, inflation is a field like air pressure (Eric Weinstein put it this way). Even if the weights and items baskets in the various categories were chosen with the best intentions it would not match anybody's experience. It would be like saying the weather in the US tomorrow will be 1056.
On top of that there is almost certainly a lot of "adjusting" of the weights and item baskets, the organizations producing the statistics have no incentives not to.
Essentially, inflation is a field like air pressure (Eric Weinstein put it this way). Even if the weights and items baskets in the various categories were chosen with the best intentions it would not match anybody's experience. It would be like saying the weather in the US tomorrow will be 1056.
On top of that there is almost certainly a lot of "adjusting" of the weights and item baskets, the organizations producing the statistics have no incentives not to.