eterm-color.ti is a terminfo source file.  eterm-color and
eterm-direct are compiled versions produced by the terminfo compiler
(tic).  The compiled files are binary, and depend on the version of
tic, but they seem to be system-independent and backwardly compatible.
So there should be no need to recompile the distributed binary
version.  If it is necessary, use:

tic -o ../ ./eterm-color.ti

(Sometimes tic puts output in etc/65 instead of etc/e.  Move it to etc/e
yourself if it does that.)

The compiled files are used by lisp/term.el, so if they are moved,
term.el needs to be changed.  terminfo requires them to be stored in
an 'e' subdirectory (the first character of the file name).