OK. I got myself an EC2 and had a go, got the same problem.
The issues is a problem with the package php-common in that it says it provides zlib.so and it doesn't.
Try the following to see that the package claims to provide zip.so
yum provides zip.so
I have been and fetched the appropriate rpm for the same architecture and extracted the zip.so and attached it to this post. If the attachments doesn 't get to the post then DM me.
Once you have the zip.so you will need to upload it to your ec2. I assume you have figured out things like that as you managed to get your moodle onto your platform. FYI I used git.
It (zip.so) needs to go in /usr/lib/php/modules
Also you need to add
to your php.ini (in /etc)
restart httpd (service httpd restart)
and that should be OK, it was for me.
I had to add the following as well (some of these from memory)
[Edit] BTW, the rest of the install went OK. I finished after posting. I also made an error on the line extension=zlib.so in my original post. (Now fixed).