Yes, you are right. The old iGrid (that we call "Classic Edition") registers in the HKLM hive for all user, and this registration requires admin rights. The new iGrid (that we call "Modern Edition") registers in the HKCU hive for the current user, and this registration does not require admin rights.
But it's possible to create HKLM registration builds for the Modern Edition of iGrid. I have just done that and updated the retail pack on the webserver. Redownload it, please. Now you should see the HKCU and HKLM subfolders in the Bin32x64 folder in the archive, and these subfolders contain the corresponding builds of Modern Edition for the HKCU and HKLM registration.