I haven't tried these sticks in particular, but I can tell you that frankincense oil (which is what they're using if the claim on the packaging is true) is often very different from the resin. There are some higher end sticks also (Tennendo's Frankincense and Yamadamatsu's Hyofu) that are close, but don't quite nail the fragrance of actual frankincense resin.

There are also a ton of different types of frankincense: different species, grades, gum content, et cetera. You might want to try a sampler to see if one varietal or another is closer to the sticks you like. Try crushing them and gently heating them.

The stick will also probably have some fragrance contributed by whatever base wood they are using.