A "Standard" user! Now, I understand exactly what you saw [if UAC was turned off: You "clicked" and, literally, "nothing happened"]. If UAC was on, you should have received a UAC prompt asking for the Administrator's password to elevate to Administrator authority.
Before I continue, I want to make certain that you understand that I am not affiliated with Eraser. I am a retired software engineer interested in privacy/security and the total disregard for it in all PC software. So, any and all opinions are mine. Less than a month ago, I discovered Eraser and liked several of its functions: the altering of folder/file names and the clearing of the Master File Table. This is the only such product that I have found that does that. And, in my opinion, it is critical because massive amounts of information can "leak" from just this source even if the contents of the files have been overwritten. However, I was disappointed in the minimal involvement of the Eraser group and total lack of any community on the Forum. And, the only Eraser 6 documentation that I have found is one incomplete and probably outdated "user guide". So, I have had to resort to educated guesses about its internal workings. Some of the Forum posts were so old and easily answerable, so I replied to several questions including yours.
That said, let me tell you how you can get Eraser 6 [6.2.2969] to run for a "Standard" user and its limitation. Most functions of Eraser 6 do not need Administrator authority to run. However, Eraser users have been struggling to get all of its functions to work especially the "Erase Free Space", which I consider critical, to run because the install process did not create the Registry entries to allow it to run with Administrator authority. So, I posted on March 23 "Install Bug & Enhancement - Registry Entries". Shortly thereafter, Eraser built 6.2.2969 trying to incorporate my findings [but missed slightly]. Eraser install now creates a String [C:\Program Files\Eraser\Eraser.exe] with the DataValue: "RUNASADMIN" in the Registry at the Keys: HKLM\SOFTWARE\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Layers and HKCU\Sofware\Microsoft\Windows NT\CurrentVersion\AppCompatFlags\Layers. Either one of these will result in Eraser running with Administrator authority on Windows 7. On all other releases of Windows, everything I have read says the DataValue must be "~RUNASADMIN". I hope Eraser tested that "RUNASADMIN" works because I can't! So, you can get Eraser to run without UAC requesting elevation to Administrator authority by using REGEDIT to "Modify..." the DataValue to something like just "x" for the key in BOTH the HKLM and HKCU hives. Don't let REGEDIT frighten you, it's a piece of cake.
If you then do a LOGOFF and LOGON, Eraser should start Automatically. And, almost everything should work as you would expect EXCEPT for the "Erase Free Space" function. [I would, of course, verify that it is the only one because I have been know to make mistakes!] For this function to run as coded, Eraser MUST run with Administrator authority [because of Windows restrictions]. And, that is impossible for "Standard" users. But, because I am unaware of even a single Application that "moves" its "temporary" and "deleted" files to the Recycle Bin where an Eraser like program could do a "Secure Delete" of them, for true privacy/security, therefore, an "Erase Free Space" must eventually be done for ALL partitions to overwrite the file contents and change the folder/file names for all deleted folders/files! An interesting dilemma, isn't it?
I will hang around for a few more days so let me know if you have any difficulties.