Nope. You don't own digital games, they are rented to you and can be stolen from you for any reason. To me tracking digital games would be the same as tracking pirated games, they are very similar except a pirated game is worth more to you...
Can you tell I hate digital games?
LOL. I see your point. I have a need for a physical "thing" when it comes to my collection.
I understand many "indies" being distributed digitally, but full-price retail games? I couldn't bring myself to pay more than a few bucks for one. I think aside from something like the Switch Zelda and Smash Bros. DLC, the most I've ever spent was to get Cuphead. And that card was given to me.
I DO count "swag" items like books, videos, toys, etc. because they are directly related to the video games themselves. If I wouldn't count those items as part of my collection, I shouldn't count the hardware either. To me, it's all one big happy family as long as A: I can physically own it and B: It is related to the games themselves (strategy guide, art book, figure, etc) or is used to play said games.