You do not need a PS, or root access, to install any of the things in that list. That said, those applications are very memory and CPU intensive and, even if you get them all installed, you are unlikely to be satisfied with the performance of the application running on a shared server account.
This kind of thing really demands more resources (PS or dedicated service) to run well. You can’t run YouTube on a $10.00 a month hosting account and have it perform well, even if some company is willing to sell you some software to perform these functions.
The DH support team will either tell you the same thing I did, or simply say, “We do not provide support for the installation/operation of third-party software”, and point you to these forums.
I can’t comment on what the people selling that script say - they are in the business of selling software, while I am in the business of technical support.
You do not have root access with your account, so if they say they require that to do the install then you won’t be able to have them install it for you.
As for my advice, I would never try to run this application on a shared hosting account.
–DreamHost Tech Support