They were not affiliate links - affiliates are URLs that contain the "tag=XYZ" bit. Sometimes people think the "ref=ABC" bit is affiliate, but it's a different tracker.
https://www.reddit.com/r/NintendoSwitch/wiki/affiliate-links
But for best practice, all you need for Amazon are the URLs up to the ASIN product code:
https://www.amazon.com/Super-Mario-Odyssey-Nintendo-Digital/dp/B072KG45JD/
https://www.amazon.com/Mario-Party-Superstars-Pre-Purchase-Standard/dp/B097PZCGMT/
https://www.amazon.com/Mario-Kart-Deluxe-Nintendo-Digital/dp/B06Y5VQMKK/
https://www.amazon.com/New-Super-Mario-Bros-Deluxe/dp/B07LFFHD7S/
https://www.amazon.com/Super-Mario-Maker-Nintendo-Digital/dp/B07SBC943H/
https://www.amazon.com/Super-Mario-World-Bowsers-Fury/dp/B08JCZKTQW/
Anything that shows up in in an Amazon URL after the /dp/ABCDE12345/ part is something that tracks or fills browsing information (e.g. search query, platform used, person sharing it).
Digital link