No it should not, as someone stated before the binaries compiled for i386 will vork in both x86 and x64 enviroment.
After you have extracted the downloaded archive use a terminal and navigate to that folder and type:
$ ls -l
Make sure it your list is the same as this:
-rw-rw-rw- 1 koenig koenig 133428 okt 2 15:30 cfe_n66u-1.0.1.3.empty.bin
-rwxrwxr-x 1 koenig koenig 922 okt 2 20:40 cfe_update.sh
-rwxrwxr-x 1 koenig koenig 78399 sep 30 20:46 nvserial
-rwxrwxr-x 1 koenig koenig 5552 okt 15 20:50 nvsimple
-rw-rw-r-- 1 koenig koenig 2718 sep 30 17:31 nvsimple.c
-rw-r--r-- 1 koenig koenig 2445 okt 14 20:24 README
except for the "koenig" part, that should instead state your username.
Then make sure you have your cfe in the same folder and then:
$ ./cfe_update.sh cfe.original cfe.new
Then post what happens here.
EDIT: Beeing a little bored I decided to flash the new cfe anway.
It worked, did a 30/30/30-reset afterwards and the router booted just fine.
router@ubuntu:~/n66u$ ls -l
total 496
-rwxrwxrwx 1 router router 133428 Oct 2 06:30 cfe_n66u-1.0.1.3.empty.bin
-rwxrwxrwx 1 router router 5116 Oct 16 08:49 cfe.new
-rwxrwxrwx 1 router router 262144 Oct 16 04:39 cfe.original
-rwxrwxrwx 1 router router 922 Oct 2 11:40 cfe_update.sh
-rwxrwxrwx 1 router router 78399 Sep 30 11:46 nvserial
-rwxrwxrwx 1 router router 5552 Oct 15 11:50 nvsimple
-rwxrwxrwx 1 router router 2718 Sep 30 08:31 nvsimple.c
-rw-r--r-- 1 router router 2445 Oct 14 11:24 README
router@ubuntu:~/n66u$ ./cfe_update.sh cfe.original cfe.new
[1/4] Dumping default NVRAM settings from your CFE...
./cfe_update.sh: 9: ./cfe_update.sh: ./nvsimple: not found
[2/4] Modifying NVRAM settings (silent step)...
[3/4] Creating new CFE...
4092+0 records in
4092+0 records out
4092 bytes (4.1 kB) copied, 0.0138105 s, 296 kB/s
./cfe_update.sh: 19: ./cfe_update.sh: ./nvserial: not found
[4/4] Checking differences between NVRAM from old and new CFE's
If you see only two differences: one is for 'bl_version' and second is a new 'odmpid=ASUS' variable then all step are done! New CFE image 'cfe.new' is prepared for flash.
it has all rights so what would not be the problem i think, im no linux expert but i did something wrong thats for sure