O Perl provavelmente está instalado, então você pode fazer
timestamp=$( some process ) # timestamp=201607130319
perl -se '
use Time::Local;
if ($ts =~ /^(\d{4})(\d\d)(\d\d)(\d\d)(\d\d)$/) {
$time = timelocal(0,$5,$4,$3,$2-1,$1-1900);
$now = time;
if (abs( $time - $now ) > 600) {
print "more than 10 minutes\n";
}
}
' -- -ts="$timestamp"