EDIT: This is not needed anymore, because PCSX2 has been released in AppImage format! Just run it like normal executable, and it should work.
Original answer:
PCSX2 can only be compiled for 32bit processors, but you are using 64bit system. PCSX2 requires some 32bit libraries to be installed, but since they would probably need to replace 64bit ones that are needed on your system, it throws error.
There are generally 3 ways how to install PCSX2 on Linux.
- Try to install 32bit libraries on 64bit system
This is what you tried to do. It works for some people, but it never worked for me since I always needed some 64bit library that couldn't be installed together with it's 32bit version.
- Install PCSX2 in 32bit chroot on your 64bit system
This is the cleanest solution since it doesn't pollute your 64bit system with 32bit libraries. This will in very simple words install 32bit system to a folder on your 64bit system, and any application that will be run from there will use 32bit libraries. This cleanly separates 64bit and 32bit system, so there are not any conflicts.
Another good thing is that chroot is not emulation, so there is not any noticeable slowdown.
If you are interested, here is link to my how-to that was created when I had the same problem.
https://jirka642.wordpress.com/2016/02/04/installing-pcsx2-on-64bit-linux/
- Reinstall and use 32bit Linux
You should probably only try this if everything else fails, since who wants to use 32bit system on modern PC?