This is probably because the Tiled (or more specifically, Qt) requires a more recent version of the FreeType library than is available on Ubuntu 14.04. I’m afraid that probably your only reasonable options are to either use an older version of Tiled or to upgrade your system.
Note that Ubuntu 14.04 reached its end of life on April 30, 2019. Since then no further security patches are provided, so I can really recommend you to upgrade your system.