Error when installing SQL Management Studio 2014 from product installer
Finally worked it out.

My issue was actually two issues. Neither one was giving good error feedback. I had to stumble on fixing them both to get the installer to work as intended.

Firstly, I reduced the list of features being installed.

/ACTION=install /QS /IACCEPTSQLSERVERLICENSETERMS /FEATURES=SSMS /UpdateEnabled=False


Secondly, I changed the length of the path leading to the SSMS installer at the time it was executed.

The previous execution path was:

C:\Program Files\Application Directory\Components\MS SQL Server\SQL Server 2014\SP1\Express\x86\SQLManagementStudio_x86_ENU.exe


The new execution path is:

C:\Program Files\Application Directory\Components\MSSQL2014SP1EXPx86\SQLManagementStudio_x86_ENU.exe


With both changes in place, the automated installation works as intended.