Dominating set in bounded degeneracy and bounded degree graphs
No it does not. The problem DOM considered by the paper seems to be the enumeration of minimal, not minimum dominating sets. Usually minimal means a solution $X$ such that there is no other solution $X'$ with $X' \subsetneq X$. The solution $X$ is not necessarily the minimum size. While minimal dominating sets can be enumerated with polynomial delay in bounded degeneracy graphs, there seems to be no guarantees that this enumeration finds the minimum dominating set before enumerating an exponential number of dominating sets that are minimal, but not minimum.