Can this be done with Xara Designer Pro X?

[Acorn]

Possibly they are Acorn.
I agree re the repel text under but I think they're getting there.
HERE'S my best shot at it

Egg, I appreciate the effort but to be clear all this is doing is scaling the page so it is not really comparable.

It is actually a better presentation and the OP can do it far, far more easily.

Acorn

[Egg Bramhill]

Hi Acorn, completely baffled here. The OP's original question was:

... with the texts adapting to the width of the browser?

Doesn't my demo do exactly that? Not only the text but the images.

... all this is doing is scaling the page so it is not really comparable

In what way?

[Acorn]

Egg, OP gave an example site. That did not scale the text, only the container.
A different mechanism is in place.

Acorn

[Egg Bramhill]

Ah! Thanks for the clarification Acorn.