0 A.D. uses the standard S3TC texture compression format, which saves at least 75% of video memory usage, improving the game's performance. Unfortunately S3TC is not supported by default in Mesa (which provides OpenGL support on Linux) due to uncertainties over patents.
The game will automatically enable the force_s3tc_enable DRI configuration option, which helps when using drivers that support texture decompression but not run-time compression. (This can be disabled via the game's configuration file: see force_s3tc_enable in data/config/default.cfg in the install directory.)
If this does not work, and the game displays a warning message, you may need to install the libtxc_dxtn library: