Error! Some required system tools when trying to apply Magento patches via SSH

The solution is to install the patch package:

yum install patch

or zypper install patch for OpenSUSE LINUX.

Then run sh the patch file:

sh PATCH_SUPEE-1533_EE_1.13.x_v1-2015-02-10-08-18-32.sh

Checking if patch can be applied/reverted successfully... Patch was applied/reverted successfully.

Repeat for all missing patches.

Note: I provided this as I spent quite a bit of time on this before realizing that the error being thrown wasn't for a previous patch but for the patch package itself.