With the strong caveat that I am still VERY new to linux, and I'm 99% certain this is not an approved way of fixing a program.... I believe I've found a way to get this program to run on Debian Jessie (updated as of 08/02/14).
In short, I made a symbolic link for "librtmp.so.0" where the "librtmp.so.1" file was located and linked to the "librtmp.so.1" file.
The reasoning was simply that both files seemed to provide the same function (according to the package summary on the debian site) and that most developers would try and keep backward compatibility if they could. That being said, the game or OS could faceplant later while I'm playing due to some issue I haven't encountered yet.
I did get a lot of "Could not unload undefined prefab" errors that listed game items like "campfire", but I had no problems selecting and placing a campfire during my two day (in-game) test. These errors only show up when running from the terminal and do not slow down the loading of the game by needing confirmation or something.
If anyone has better suggestions or tips, please feel free to chime in.
For the record, Installing Linux Mint (easiest) or recompiling rtmpdump is the better solution - I just like to tinker and haven't tried recompiling yet.