There’s a thread on Slickdeals that provides data points stating that gift card purchases in the Samsung Pay store are triggering the $5 statement credit from the Shop Small Amex Offer. This comes on the back of Fluz and eGifter purchases also triggering the Amex Offer.
I can understand why eGifter and Fluz would work, but it’s surprising that Samsung Pay would work as I wouldn’t have expected that to be classed as a small business. If you’re planning on buying gift cards, I’d therefore be more cautious about using Samsung Pay to do that as statement credits received from those transactions might be more prone to being clawed back by Amex. Besides, at least with Fluz you can earn additional cashback while eGifter offers points.