I think it is wrong to totally discredit mobile games like they aren't "real games." But my understanding is that there are millions of mobile games, many of them cheap cash-in's and IAP filled crap. It would be impossible to catalog them all and even harder to differentiate between paid versions and the "freemium" versions. You mentioned Square-Enix and DS game ports, but where do you draw the line between what games would be acceptable to the database and which games aren't? You couldn't even base it off of "best selling" mobile games because crap like Clash of Clans which is pay-to-win is at the top of the charts. Same for junk like Candy Crush Saga or that stupid crap they have Ahnold advertising.
Personally, I'm looking at deleting all of my "digital" game titles from my collection because really, I don't own them. The purpose of a database cataloging a "collection" revolves around tangible goods. At least for me anyway. If I counted all the "digital" games I have downloaded on my Wii emulator, I would have a collection rivaled only by the Flea in sheer numbers. But those ROM files, just like WiiWare, PSN, Xbox Live and Steam games are just virtual bits stored en-masse on a HDD.