This is correct - random forests discretize continuous variables since they are based on decision trees, which function through recursive binary partitioning. But with sufficient data and sufficient splits, a step function with many small steps can approximate a smooth function. So this need not be a problem. If you really want to capture a smooth response by a single predictor, you calculate the partial effect of any particular variable and fit a smooth function to it (this does not affect the model itself, which will retain this stepwise character).
Random forests offer quite a few advantages over standard regression techniques for some applications. To mention just three:
- They allow the use of arbitrarily many predictors (more predictors than data points is possible)
- They can approximate complex nonlinear shapes without a priori specification
- They can capture complex interactions between predictions without a priori specification.
As for whether it is a 'true' regression, this is somewhat semantic. After all, piecewise regression is regression too, but is also not smooth. As is any regression with a categorical predictor, as pointed out in the comments below.