How do you easily determine which results link found on Wayback Machine actually represents the store page so that art can be confirmed?
This is indeed hard, now that the marketplace is closed. I used to be able to google something like: "
[Game Title Here] site:https://marketplace.xbox.com/en-US/Product" which would lead to results like this:
https://www.google.com/search?q=fatal+inertia+site%3Ahttps%3A%2F%2Fmarketplace.xbox.com%2Fen-US%2FProduct (if searching for the game "Fatal Inertia"). But now that the Marketplace is closed, you can't search against that "site" anymore for the official listings, as the site is no longer online, and there will be no results anymore (as can be seen if you click the above Google Results link).
I found on the Wayback Machine/Internet Archive,
my link above works with "trailing" wildcards only according to Archive documentation/FAQ and their API documentation as well, hence having to put in the beginning of the title only and test to see if I can figure out the way Microsoft formatted the title in the URL. So I usually start more vague, and as I search and confirm, I get more specific (e.g. start with "gears*" then based on results, update to "gears-of-war*" or "gears-of-war-2*" etc. OR if no clear results try "GOW*" or "GOW2" etc.) B/C it's not always certain how the URL was formatted by Microsoft back in the day (e.g. was it "Gears-of-War-2" or "Gears-of-W2" or "GoW2" etc.), especially b/c they often had no consistent way to handle it. A tricky example is Lego Batman 3... most of the Lego games start with "lego" at the beginning of the title (including Lego Batman and Lego Batman 2). But for Lego Batman 3, they only list it as the subtitle "Beyond Gotham" so searching "lego*" will not get you the right results.
However, a quick and dirty way to find the relevant game listing out of the 965 results for "
http://marketplace.xbox.com/en-US/Product/gears*" is to sort by "Captures." The ones with the most captures will appear at the top, and those are almost always the general Game listing, as opposed to smaller DLCs, themes/avatars/gamerpics, or archived affiliate links to the game listing, etc.

In the case of a "gears" search, the top ones should be the main Game Listing for Gears of War, Gears of War 2, Gears of War 3, etc.
Then you can see the "ID" for the game is consistent, despite the title formatting, or if they have multiple ways to format the title.
Example: Gears of War 2:
- Gears-of-War-2 has the ID 66acd000-77fe-1000-9115-d8024d53082d
- Gears-of-W2 has the same ID 66acd000-77fe-1000-9115-d8024d53082d

So if you can't find the main game listing via the above method, but you can find the "ID" from other URLs (like URLs to smaller DLC or Avatars/Gamerpics related to the game, etc.) you can use the search filter to narrow to just URLs for this specific game, and that narrows the search even more, to help find the main game listing.

This search narrows the 965 results to 214.
Granted these methods are really only needed for
major games like Gears & Halo, etc. b/c they have
soooo many add-ons, gamerpics, trailers, cosmetic items, sequels, etc. Most games only return a few URLs and it's easier to find what you're looking for right away.