Or does rare only figure for physical copies?

Rarity exists pretty much exclusively physically, basically. However, if 2 people buy the game, and it gets pulled from whatever online storefront, then the piece of hardware (or perhaps account) that game is stored on can be rare.

There are an infinite amount of purchasable digital copies of Shantae on 3DS Virtual Console, for example, so there's nothing rare about it.

Digital games can't really be rare. As long as it is online, it is limitless and easily able to be picked up by anyone. Only rare time is like Flappy Bird for a short time and PT. PT is the rare case of a digital game being rare.

Well digital games are always readily avaliable, so rarity doesn't really apply.

Interesting you guys think that.
Maybe the concept of rarity deserves a little reevaluation in the digital download age? I mean the things readily available still have a price. A copy is only really "made" when it is bought.

they cane be pirated and uploaded online to make infinite amount of copies

Rarity or rather collectibility pretty much always includes the box. Digital only games aren't collectible (so far). You can pirate and copy them as much as you want. PT can be cracked and distributed.

Of course it can still be rare to find if only a few people buy it. Yet would you pay extra for a rare steam key?

I just downloaded the Shantae ROM and copied it over a thousand times. For real, because I'm crazy. If I burn that to a DVD, can I sell it for a million dollars?

How rare is PT really? I mean millions of people likely downloaded the demo.

Then if I press a 1000 discs with the ROMs, can I get a billion dollars? I mean, the investment may be worth it.

The ROMs have never been played. Though I may have made a mistake by unzipping them. Are unzipped ROMs kind of like sealed cartridges? Could even fit more ROMs per disc if I redownload.