I don't understand how this can be a valid comparison, unless you bought games planning to never play them, just check them off against your list? That seems like a very minor use case. This would be like people saying they "collect" Kindle books or itunes music.
Collecting is based on the idea of scarcity, either real or contrived, and digital plus not even owning the object makes that both impossible to be true and near impossible to pretend.
It's not a minor use case. According to Forbes[1], 37% of all games purchased on Steam never get played.
Collecting definitely doesn't have to be based on scarcity. Board games aren't scarce (some are long out of print and rare, yes, but most aren't) yet I know people with vast collections (I myself have about 500 board games, and only maybe 3 or 4 are rare enough to be worth any significant money beyond its retail price). If 500 games is not a collection, then what would you call it?
500 board games isn't even necessarily a lot for a collector (it is for me, as I don't have the space to store them anymore and need to sell like 200 of them, but yet I keep compulsively buying new games anyway, I bought 2 more just this past week). I know another guy in my area that has over 2000 board games in his basement.
And I (and many other board game collectors) don't play the games anywhere near as much as we buy them. We may justify the purchase with 'oh this would be good for this group someday' but mainly it's just an excuse to get it onto our shelves.
Before I started playing board games solo, I'd say about 80% of the games I bought I hadn't played since I bought them, sitting on the shelf (for years) for the possible right board game night in the future for them to be played. Or I played the game since, but someone else's copy, since between my friends we often have 2-5 copies amongst us.
Now I mostly buy games I can play solo, and I've played a good chunk of my new purchases the past two years at least once.
Buying yet never playing is so common in board games, in fact, that there's a term for those unplayed games: 'The Shelf of Shame'[2]
Many people buy games, books, even music and movies with the “I’m interested and will get to it someday”.
It’s more rare for someone to explicitly buy something with the firm intention never to play it (and usually that is a second copy they want to keep pristine).
Most of my unplayed steam games are that - oh, $5? I’ve heard of that and want to play it someday, I’ll grab it now.
I mean, that’s my justification too, but let’s be honest, I won’t ever have the time or energy to properly play half of the things I buy, and I’d save a lot of money if I took that into account before I bought them.