In the current version of the steam.sh script†, the variable INITIAL_LAUNCH is set as follows:

# See if this is the initial launch of Steam
if [ ! -f "$PIDFILE" ] || ! kill -0 $(cat "$PIDFILE") 2>/dev/null; then
    INITIAL_LAUNCH=true
else
    INITIAL_LAUNCH=false
fi

This variable is then used in the following lines:

Line 453:

if [ -z "$INITIAL_LAUNCH" ]; then

Line 582:

if [ "$INITIAL_LAUNCH" ]; then

Lines 769 through 773:

if [ "$INITIAL_LAUNCH" -a \
      $STATUS -ne $MAGIC_RESTART_EXITCODE -a \
      -f "$STEAMSTARTING" -a \
      -z "${STEAM_INSTALLED_BOOTSTRAP-}" -a \
      -z "$STEAMSCRIPT_OUTOFDATE" ]; then

The value of the variable makes no difference in any of these tests.
In the first two cases, the test always succeeds. It would only fail if the variable were unset or empty.

Previously, this script didn't set the variable to the string "false" as it does now; it simply didn't set the variable. That effectively worked, unless the script was started with an environment variable with that name set to a non-empty string, in which case it'd have the same behavior as it has now (always testing positive).

A clean way to fix this is to replace all tests with:

[ "$INITIAL_LAUNCH" == true ]

Remember: the strings "true" and "false" don't have any special meaning.
They might as well be "foo" and "bar," for all bash cares.

Also, consider following the practice of using lowercase names for script-local variables, i.e. stuff that's not passed as an environment variable to child processes.

† steam.sh info:

Length: 22499 Bytes
Modified: 2015-02-05
sha1sum: 79fed5201bfd210216cd47eaab9361e5205cc025