First, check if the package manager has a package called libzip4 (that's the name in ubuntu 16.04), or maybe it's just called libzip. I recommend not symlinking versioned libraries to the wrong version because they change the version when they have made changes making them incompatible. It might run, but do something unexpected at runtime.

If mint doesn't have the right version of libzip, then recompiling is much better. I'd try compiling it myself according to these [instructions](https://github.com/OpenRCT2/OpenRCT2/wiki/Building-OpenRCT2-on-Linux). I assume the ubuntu instructions won't need many changes. For opensource games I usually download the git repository at latest release tag, and compile myself if the distribution I use doesn't provide the latest version fast enough.

Hmm strange, I'm running Linux Mint 18.1 and the package "libzip4" is installed by default.

If you want a quick easy solution, I made you a portable version of this library (it was taken from the Ubuntu 16.04 repo) with which you can run the game without installing the package in your system.

The Link is from my google drive: https://drive.google.com/file/d/0Bw5Xv02Yq2HrcnE1ekdPWF9VWGc/view?usp=sharing

Just extract it into your OpenRCT2 folder and click on "play_orct2.sh" to run.

Disclaimer: I know some people might be wary about downloading files from strangers. I've been doing portable libraries for the past couple of years for the GOG community, normally targeting *buntu / *buntu based distros.

A few of my other projects:

https://www.gog.com/forum/general/modern_linux_patches_for_id_software_classics
https://www.gog.com/forum/unreal_series/unreal_tournament_2004_easy_setup_for_linux
https://www.gog.com/forum/unreal_series/unreal_tournament_99_goty_easy_setup_for_linux
https://www.gog.com/forum/mount_blade_series/mount_blade_warband_linux_mint_easy_setup

Thanks for the suggestions.

I think I managed to install libzip4 (it's not in the Mint Repos for some reason) - I no longer get that error when launching the binary, instead it now says:
dodrian@dodrian-desktop ~ $ openrct2 
/home/dodrian/.config/OpenRCT2/bin/openrct2: /usr/lib/x86_64-linux-gnu/libstdc++.so.6: version `GLIBCXX_3.4.21' not found (required by /home/dodrian/.config/OpenRCT2/bin/openrct2)
/home/dodrian/.config/OpenRCT2/bin/openrct2: /usr/lib/x86_64-linux-gnu/libstdc++.so.6: version `CXXABI_1.3.9' not found (required by /home/dodrian/.config/OpenRCT2/bin/openrct2)
/home/dodrian/.config/OpenRCT2/bin/openrct2: /usr/lib/x86_64-linux-gnu/libstdc++.so.6: version `GLIBCXX_3.4.20' not found (required by /home/dodrian/.config/OpenRCT2/bin/openrct2)

No idea what that's about. Ran apt-get upgrade and checked that libstdc++6 is installed. Still no luck.

I tried following the build instructions from the Wiki, it appears to have come back to a libzip error again.

Spoiler, click me

dodrian@dodrian-desktop /home/media/OpenRCT2-0.0.7/build $ cmake ..
-- The CXX compiler identification is GNU 4.8.4
-- Check for working CXX compiler: /usr/bin/c++
-- Check for working CXX compiler: /usr/bin/c++ -- works
-- Detecting CXX compiler ABI info
-- Detecting CXX compiler ABI info - done
-- Unsupported CFLAG: -Wno-error=date-time
-- Unsupported CXXFLAG: -Wno-error=date-time
-- Unsupported CXXFLAG: -Wnull-dereference
-- Unsupported CXXFLAG: -Wsuggest-final-types
-- Unsupported CXXFLAG: -Wsuggest-final-methods
-- Unsupported CXXFLAG: -Wsuggest-override
-- Unsupported CXXFLAG: -Wduplicated-cond
-- Unsupported CXXFLAG: -Wredundant-decls
-- Unsupported CXXFLAG: -Wignored-qualifiers
-- Unsupported CXXFLAG: -Wstrict-overflow=1
-- checking for module 'libzip>=1.0'
--   package 'libzip>=1.0' not found
CMake Error at /usr/share/cmake-2.8/Modules/FindPkgConfig.cmake:283 (message):
  A required package was not found
Call Stack (most recent call first):
  /usr/share/cmake-2.8/Modules/FindPkgConfig.cmake:337 (_pkg_check_modules_internal)
  CMakeLists.txt:318 (PKG_CHECK_MODULES)


-- Configuring incomplete, errors occurred!

Unless y'all think I'm doing something obviously stupid I guess I'll stick to running RCT2 under wine for now. God bless PlayOnLinux!

@Avehicle7887

Thanks for trying to help! I saw your post after writing my previous reply, your script is giving me the libstdc++.so.6 errors again :-/

Wondering what I've done to mess up my system :D. Maybe it's time to try Arch after Liam's articles recommending it!