In the second quote, the phrases "in their official capacity" and "as the position of the United States" are doing a lot of heavy lifting.

The EO is going out of its way to broadcast that its purpose is to establish a unitary policy position of the executive branch that stems from the President, rather than having "independent" agencies providing contrary position from within "in their official capacity" "as the position of the United States." The logical leap from there to "the President's (unrestricted) opinion is the law (without reference to Congress or the Courts)" is vast.

The EO does not bear on the balance of powers between branches of government, but on the ability for the executive branch to function as a single entity within that balance, rather than a multiplicity of quasi-"independent" agencies.

The disincentives that have always prevented the executive from blatantly violating the law are still in force and unchanged. They have been functional through 250 years of Presidents testing the limits of their authority.