On James Hyde's example of non-orderable subgroup of Homeo(D, partial derivative D)

In Ann. Math. 190 (2019), 657-661, James Hyde presented the first example of non-left-orderable, finitely generated subgroup of Homeo (D, partial derivative D), the group of homeomorphisms of the disk fixing the boundary. This implies that the group Homeo (D, partial derivative D) itself is not left-orderable. We revisit the construction, and present a slightly different proof of purely dynamical flavor, avoiding direct references to properties of left-orders. Our approach allows to solve the analogue problem for actions on the circle.