Hi Caccio.
My brother is a world champion ccg player, so I do understand the frustration, as they're games he's enjoyed but I've never got into due to lack of accessible versions the moment.
As As Magurpt said, the most extensive thing we've got ccg wise at the moment is crazy party.
Crazy party is a combination of two games, both of which can be played online against other people, once you've unlocked enough to play with.
one is a marrio party series of minigames, which range from arcade to interlectual challenge,s the other however is a card based battle mode which functions like a ccg.
There are 19 different gyms to beat with computer opponents, and once you've beaten your first few gyms and unlocked enough cards you can make decks and play online.
I believe currently there are 18 different elemental card types (the elemental rules are slightly pokemon like),around two thousand cards or so, with new ones being released in updates. Card affects include various attack and damage types, as well as status effects, parry cards, reaction cards that react to certain attack types, and also cards for doing things like drawing from your deck.
Certainly this is the best accessible ccg game had so far.
There is then Aprone's triple triad game. This doesn't have online play yet, but it will hopefully be added soon. The game is basically a version of the triple triad minigame from the final fantasy series and some other squaresoft titles.
There is then the text based yugio simulator. I don't have as much experience with that, but you can check the topic in the new releases room. I gather that it is still something of a work in progress, though how that progress is I'm not sure.
There used to be a browser based ccg called I believe abandoned lands, who started with some access updates (although navigating the site was a bit of a pest), but they seemed to have slightly dropped off the map.
There are some other projects in progress, I still have hopes of dreamquest on Ios, which is a combination ccg and rpg, but concrete as yet I'm afraid other than the games I mentioned.
As to access, yes, theoretically a computerized game similar to hearthstone could! be made accessible, but in practice getting large companies interested in accessibility is pretty difficult, though I do have hopes for something indi developed.
other sources of competing online though there are various places to look.
Crazy party rocks, both the battle mode with it's ccg mechanics and the minigames too, and I can say playing online there is a great experience.
there are also several places you can play traditional games like poker, hearts, spades, euchre, monopoly etc. Namely rs games client, quentin C playroom and blind adrenaline, though none have actual ccgs as yet.
Finally, I am not sure if you have access to Ios device, but there is a lot of competitive play stuff with online capabilities on that platform, plus, with the Ios device sensitive analogue inputs, eg, gyroscope, there are games which are a lot more practical.
blindfold games even have a pool game where you use your finger as the cue, though how accurate it is I don't know.
There is also lost cities, which, while not a ccg is indeed a rather unique card game which you can play against other people online.
Btw, I also wonder, did you see the option in puppet nightmares for online matches? I don't mean the automatic hunting where you essentially fight another person's soul puppets controlled he computer ai, I mean the actual online version against others.
that one really struck me as similar to a ccg, given the amount of factors involved battles,, disciplines, weapons, formations, puppet skills, stealing etc.
Hth.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)