I get the author's not trying to write a watertight syllogism, but the point he's trying to make (his last sentence) doesn't follow from the obvious fact that beliefs can influence each other.

Christianity and worldviews typically associated with the 'east' (as I've seen them discussed here and elsewhere) disagree in both their view of the 'building blocks' of reality, and in their 'big picture' view. They disagree on base questions like if there is really a "you", or whether change is real, or whether the material world is real, or whether multiplicity is real, or whether the truth of A implies the falsehood of not-A, and so on. (I've heard all of the above answered in the negative here.) And they disagree on 'big picture' things like the goal of human existence, the nature of the Absolute, what it is to live a good life, whether evil is the result of illusion or is (in addition to this) a defect in the will and caused ultimately by an indescribably malevolent being, whether a human being can reach a 'blessed' state by his own power, etc.

So the differences are vast and essential, on both the macro and micro levels. The fact that some beliefs and practices influence other beliefs and practices doesn't change this.

(The emergence of the "18 year old who just read Dawkins for the first time and thinks science disproves sky-daddy lolz" atheists on this thread is also most unfortunate.)