mysqldump: ERROR 2006: MySQL server has gone away when attempting to push data to RDS instance
The error
mysqldump: Got errno 32 on write

simply means you ran out of space.
The question is: Where is the space issue coming from ???
--order-by-primary

Using this requires creating a temp table in the folder configured in tmpdir
Bigger mysqldumps need a much larger tmpdir when using --order-by-primary
If you get rid of --order-by-primary, you can handle bigger dumps.
You just asked

what are the implications of removing --order-by-primary ?

There are improvements to the dump's creation
IMPROVEMENT #1 : Faster Dump
Every time you dump a table using --order-by-primary, a temp table must be created. That can pause the mysqldump on the source side. Such pausing will never occur anymore
IMPROVEMENT #2 : No bloated indexes
When you load a table in PRIMARY KEY order, it can generate up to 45% additonal wasted space in the indexes due to lopsided page splits in your BTREE indexes.

Jun 28, 2012 : Benefits of BTREE in MySQL
Oct 26, 2012 : How badly does innodb fragment in the face of somewhat out-of-order insertions?
Nov 26, 2012 : Does the Int type primary key insert order affect query performance in MySQL? (discusses this from MyISAM point-of-view)

IMPROVEMENT #3 : AUTO_INCREMENT PRIMARY KEYs
If the majority of your tables has a single integer that is auto incremented and is the PRIMARY KEY, the table is already ordered. No need for the overkill of --order-by-primary
Concerning your next comment

I removed --order-by-primary, got the same error at the same time :(

Please make sure you have extra diskspace on the RDS Instance. Why ?
It is possible for a dump to be bigger when reloaded, especially when exacerbated by having keys ordered.

Sep 09 , 2016 : mysqldump: ERROR 2006: MySQL server has gone away when attempting to push data to RDS instance
May 01, 2014 : Why would the size of MySQL MyISAM table indexes (aka MYI file) not match after mysqldump import?