Evolution does not require randomness as such, the way that quantum theory requires real contingency. The whole theory of evolution can exist just fine if randomness simply means “some laws we haven’t figured out yet”. Now if there is a complete system governing evolution, there is certainly a great number of things to figure out: the development of mammals, for example, required an asteroid striking the earth; and the development of carbon molecules can only happen in the heart of a dying star. The arising of life required the some very particular actions of the whole universe, and so to understand the laws of the system that generated life would require knowing the laws governing the whole universe in a very particular and well defined way.
Dawkins does deserve credit or popularizing the idea that evolution is is actually a system and therefore is not fundamentally random. The question of how action directed by intelligence fits into his is a separate point- for St. Thomas, intelligent action for an end is given simply because there is an order of one thing to another at all. The mere fact that that organisms have an intelligible order to their environment at all- that they are warmed by the sun, say, is a perfect instance of what St. Thomas calls an action that is done for the sake of something, as is clear from Summa Contra Gentiles III: 2, where St. Tomas says that certain things act for an end when:
The force of any agent tends to some determined thing, for a certain action does not proceed from any old power- but heating is from heat, and freeing is from coolness, which is why actions differ in kind because of acting in different ways.
Omnis autem agentis impetus ad aliquid certum tendit: non enim ex quacumque virtute quaevis actio procedit, sed a calore quidem calefactio, a frigore autem infrigidatio; unde et actiones secundum diversitatem activorum specie differunt.