So, just to make it clear, the main difference in this paper is adding a small amount of noise to each update? I'm a little frustrated that I read through the whole paper and still am not sure about this.
The actual changes this led to are:
1) As you mentioned, they added noise. But notably, they state it was "designed carefully" to conform to the requirements of SGLD and they detail how they designed the noise.
2) They simplified the original operations of "move, split, clone, prune, and add" and their related heuristics, into a single operation type. They do so guided by existing knowledge about MCMC frameworks, leading to a simpler model with stronger theoretical underpinnings (huge win!).
3) Adjustments to how gaussians are added and pruned to better fit with the new model. This seems more like housekeeping rather than something novel in and of itself.