The tool is packaged in Microsoft Installer, so you can use the MSI switches with the .msi files. For example

RQMExcelImporterX64setup.msi /quiet /log install.log

Since the files are not digitally signed, you are most likely faced with a security warning prompt when launching the command, which basically breaks this "silent mode". To address this, you will need to make some changes to the machine(s). This involves security concerns so I leave it up to you to decide whether to go ahead with such changes. You can search "MSI bypass security warning" to find out the instructions, and the following blog is one example.
http://blogs.msdn.com/b/askie/archive/2009/06/19/how-to-bypass-the-security-warning-unknown-publisher-with-the-checkbox-always-ask-before-opening-this-file.aspx

Hi, Stan

According to https://jazz.net/wiki/bin/view/Main/FrequentlyAskedQuestions
===
    Is an unattended install possible? For an unattended installation the following command line can be used, this will not install the KB908002 update which is required, and should only be used once the update has been applied.:

msiexec /quiet TARGETDIR="<new location>" /i RQMExcelImporter.msi
==
KB908002 will be available when you unzip the downloaded RQMExcel/WordImporter install image.

As per
https://jazz.net/wiki/bin/view/Main/RQMExcelWordImporter#Install_Guide,
you will need local admin permission on Windows to install this add-in.

The below article provides the switches you can use for Msiexec command line options:

https://technet.microsoft.com/en-us/library/cc759262%28v=ws.10%29.aspx

I tried the below command line before and it worked for me(v4.0.x):
msiexec /i RQMExcelImporterSetup.msi /qn /norestart /Lime excel_logfile.txt ALLUSERS=1

(ALLUSERS=1 is corresponding to everyone option in GUI install mode)

I hope these info helps you to do the silent install.