My goal is to classify dense forest tree species using drone images. Is it possible to classify dense cloud points? If yes, in what way and in what software?
Yes, it is possible, to identify tree species based on LIDAR scanning. Of course first the programme must learn the species present in the area of interest. You may read more on this subject e.g. here (but there are many more papers and software to consider):
Michael J. Parlow and Trevor B. Hooper "Using LiDAR to identify tree species", Proc. SPIE 10790, Earth Resources and Environmental Remote Sensing/GIS Applications IX, 1079018 (11 October 2018); https://doi.org/10.1117/12.2326569
Not that I am aware, you could maybe do it from the associated imagery. Check your linked paper, if they use only the first return data of the lidar it may be possible, but I doubt it and you likely do not have the point density that lidar has even if it is only first return.