Indeed, there's a lot of dependencies that will prevent Spriter from starting out of the box on almost every Linux out there (tested on Ubuntu 10.04, 12.04 and 14.04, failed on all of them), and most of those libraries should be bundled with the application. Once I made Spriter work on my Archlinux, I took the liberty of packing it up as an AppImage, and uploaded it here.
It's a pretty big package (37.50 MB) compared to the original package (Spriter_free32.tar.gz, 3.3 MB), but it's not really that big for today's standards on Internet speed and storage capacity, and it should create a much better user experience (at least it works out of the box on 32bit Ubuntu 10.04, 12.04 and 14.04 LiveCDs). Besides, it packs even the static linker in a overzealot attempt to make the package as portable as possible, but other people usually just build the app in an old enough distro and pack only uncommon libraries (like libMagick++ or libQt*) while keeping common ones (like libc), or build static binaries (like the Godot engine (which I hope Spriter supports in a future!!) guys, that pack just one static binary without dependencies (although if you use Qt you can't link statically without an expensive pro license, so bundling the libraries along with your app would be the only way)