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You don't need one if you have other means of attaching your 2.5" SSD to the back wall of the iMac case (like industrial strength Velcro or 3M VHB tape), but the bracket you mount into is a 3.5" space for a full sized desktop drive and SSDs are 2.5". Thus the adapter... just to mount the drive into the bigger bracket area.
This guide is way more than needed for the display replacement. Until it gets edited down, all you need to do is steps 1-3, 12, 22-24, 28, 31-35 from the "upper case replacement" guide (which is apparently what this guide is right now, instead of a display replacement guide as it is labeled).