This is my thinking, too. I was always under the impression the entire 1st print run of NP #1 was given to Nintendo Fun Club subscribers. But if this wasn't the case, I can understand why Nintendo would want to emphasis the "Free Sample Copy" message for the subscriber giveaway issues. This would be easy to semi-confirm if anyone purchased NP #1 off a retail magazine rack way back when. I recently won the non-variant NP #1 thanks to RetroMags' current contest (thanks again, Phillyman!), and thought I'd share some more differences I found when comparing the two covers.
The variant is labeled "PREMIERE ISSUE 1988" on the cover and "PREMIERE ISSUE 1988" on the spine. The non-variant is labeled "July/August 1988" on the cover and "JULY/AUGUST 1988" on the spine.
The Nintendo Power logo and logo trademark symbol are larger on the non-variant.
Thanks in part to a narrower footer bar, the non-variant displays slightly more artwork vertically. The variant displays more artwork horizontally.
This may be related to the poor condition of my variant copy, but it appears the non-variant features better coloring - the background gradient is more teal than light-blue, allowing the foreground objects (especially Mario) better definition. Also, Mario's face has better flesh-tone.
Perhaps most interesting, the cover's Super Mario 2 sub-text reads "18-Page Spectacular" on the variant, but "20-Page Spectacular" on the non-variant.
I'll probably compare the contents of each issue sometime, as the 18 vs. 20 page difference has me intrigued. Probably just a typo/correction, though.
Here's a comparison of the two covers. (I know Retromags already has a scan of non-variant NP #1, but I thought everyone would like to see the differences when the covers are scanned with matching scanner hardware/image compression.)