Hi HomerJ,
You should not need admin rights on the local systems unless you are trying to register the clients (necessary to use third party add-ins such as Excel and Word add-ins). From the screen shot it looks like the platform loader is being blocked and this shouldn't be a matter of admin rights needed but the file being allowed to be passed to the client. It could be something as simple as placing the ALM URL in the local trusted zone and lowering the UAC level for the system to the lowest setting ''do not notify''. You should only have this issue on the initial install of the client as once the platform loader is downloaded and installed it shouldn't need to be further downloaded until the ALM system is updated or patched. It looks like the browser is blocking the download or possibly an anti-virus blocking the file (the lowering of UAC settings, turning off anti-virus scans or setting an exception for the ALM files, and adding the URL to the trusted zone on the browser are recommendations for the initial install) and shouldn't need to be done after that initial. Depending on your internal security these may not be allowed or they may be needed to be accomplished through a group policy by your IT department.
As for another option. You can create an MSI, using the MSI generator (it can be obtained through the Microfocus marketplace (accessed through the tools option at the initial screen) and then have this MSI pushed to all your clients by the IT department. The downfall of the MSI is that it will need to be regenerated and pushed out each time the ALM system is updated or patched so it reflects the latest information for your ALM server.
Hope this helps in assisting with the issue or giving you areas to look at,
Dan