I think we handle digital games splendidly around here- they are listed, but in seperate chunks from the physical stuff. When you click on your collection breakdown, You get Games and Games- Digital. When you look at your console list, the online services are their own category. If you consider your physical & digital of equal importance, it's a lil' hoop-jumpy, but it's still just a few clicks & a calcuator to get a total. Plus it's more reflective of how other digital-only options work (like Steam or GoG).
I'm not really a fan of digital games, but I do list the ones I have here. It provides a way for me to show people what games I have available if they want to play something. No, I can't lend a digital game... but there's only a few people I'm willing to lend to. Basically, if you wanna play it, you're visiting. Most of the logic people use to not count digital- 'you can't sell it, it's stuck on that specific hard drive, what if it fails?, etc' seems flawed to me. Physical media fails all the time, and the vast majority of this data can be moved to other drives if you change systems. Unless you're trying to sell, it's not all that different (if a lot more work) from handling physical media- and I don't sell, so what do I care?
I'm kinda curious though for digital game collectors
I know of people who have certain games as a paid download on multiple consoles
say chrono trigger
eshop 3ds
eshop wii
wii u eshop
steam
phone
Are you going to list chrono trigger as a digital copy 5 times or 1 time
I"m just curious everyone collects differently after all
For the example you give, I'd list each game separately. It's no different than listing physical games from multiple systems (say someone has FF13 on PS3 & Xbox 360), or keeping label variants.
Where it gets weird is cross-play... like how some games bought on Vita automatically unlock on PS4 & share save data. I have no digital cross-play titles, so I'm not sure if I'd list the games twice or not. I did list Journey again when it gave me the re-download option on PS4, but that's becuase it has a separate trophies list, so it works like a new copy instead of a simple transfer.