Sylvia,
The answer is even simpler and has been discussed long ago, over 100 years ago in fact. Gill in his comenetary of this text said:
Ver. 31. And these [are] the kings that reigned in the land of Edom, &c.] In the land that was afterwards called the land of Edom; for this laud was not so called when these kings began to reign: for, according to Bishop Cumberland {f}, and those that follow him {g}, these were Horite kings, who, after their defeat by Chedorlaomer, #Ge 14:5,6; in order to secure themselves the better from such a calamity for the future, set up a kingdom, and which appears, by the following account, to be elective; and so Maimonides {h} observes, that not one of these kings were of Edom: and these were,
before there reigned any king over the children of Israel; and there being no kings over Israel until many years after the times of Moses, hence some have thought these words are inserted by some other writer after him; but there is no need to suppose that; for Moses knew, from foregoing prophecies and promises, that kings would arise out of them and reign over them, #Ge 17:6 35:11; and this he was so certain of, that he himself, by divine direction, gave laws and rules to the children of Israel respecting their future kings, #De 17:14-20; besides Moses himself was king in Jeshurun or Israel, #De 33:5, so that it is the same as if he had said, these are the kings that reigned in Edom, before this time.
{f} Orig. Gent. Antiq. p. 1-24.
{g} Bedford in his Scripture Chronology, and the Authors of the Universal History.
{h} Morch Nevochim, par. 3. c. 50. p. 510.