Is rolling of biased dice random phenomenon?
Yes, you are correct. Rolling of dice is (almost always) a random phenomenon. In case of biased v unbiased dice, the difference is solely in the probability distributions. For unbiased the distribution must be uniform, for biased it can be anything we want.
The only case where biased dice stop being random phenomena is when we load them in such a way that they always produce a predetermined number (or a specific sequence).