@Wesley:
At 10.1, only 64-bit versions of the database are supported. The ST_Geometry library is 64-bit only; I'm pretty sure that it will not work with a 32-bit installation of PostgreSQL.
As a tip for when you install a 64-bit database cluster...I'm assuming that since you installed PostGIS that you want to use the geometry type for data storage(?) If so, be sure to pre-create your database using the PostGIS template before running the tool to create a geodatabase. The Create Enterprise Geodatabase tool uses the default PostgreSQL template database to create the database, which will not include PostGIS. (You'll still have to copy over the ST_Geometry library for the tool to run, but you don't have to use the ST_Geometry storage type once the geodatabase is created.)
@Ryan:
You should be able to run pg_config when logged in as the postgres user to determine which location to place the st_geometry.so file. (I say should because Ubuntu isn't technically supported, so I don't know for sure this will work in this case.) Also, be sure you copied the 9.1 version of the file since you indicated that you are using PostgreSQL 9.1.
@Bryan:
The topic you mention is a tutorial, specific to one particular OS and DBMS version; we wouldn't want to link to it from the error since it isn't applicable to all situations. HOWEVER, if the message still says "You must copy the latest ST_GEOMETRY and dependent libraries to the PostgreSQL software location...", we gotta fix that, since there aren't any other libraries you need to copy. I'll check on that and open a bug to fix the message if necessary.