Welcome to Argent Dawn, Muzzle!
Zagkush is referring to the installation destination 
Be sure to install the addon in \World of Warcraft\_retail_ and not in _Classic_. You’ll get two folders, one called totalRP3 and one called totalRP3_Data. (I have tons of others but this is the only one you’ll really need for RP.)
Install TRP3 in \World of Warcraft\_retail_\Interface\AddOns
If this is problematic you can just remove the TRP3 files you downloaded from the website, and instead use the addon manager integrated in Twitch. It’s very easy that way to get addons and keep them up to date so I’d recommend that.
You can get TRP3, Listener (including Snooper, they are not separate addons), and pretty much everything else as one-click-install addons from the Twitch WoW addons library.
^ Twitch addon manager interface
^ The glorious Snooper window of the Listener addon
Note also that you can configure your regular chatbox to stop showing you NPC chat or put it into a separate tab so the NPCs don’t spam away your RP interaction.
You can also create additional chatbox tabs so you can easily toggle between everything, or G chat only, or RP only, or a list of recently looted items, etc. Click here for a chatbox configuration guide.
^ Untick all the Creature Messages boxes for an NPC-proof chatbox
One addon that hasn’t been mentioned yet but that will probably make things easier for you and others reading along: WIM (Wow Instant Messenger).
It takes whispers out of your main chatbox and into separate little boxes that you can easily close and re-open. I used to constantly forget names or spend ages scrolling so this is a godsend for me, especially as a DM.
^ WoW Instant Messenger
Finally, lemme highlight this useful comment that was mentioned by Lintian above.
Check out the full reply and in particular the Guide to roleplay for newcomers - #16.
Again, welcome aboard Muzzle and if you’ve any more questions, go right ahead!
EDIT:
Yes, unfortunately. They do it to make it impossible for others to track your alts, I suppose.