Forgive me, I've said how it's not "just another one of those" twice, but I haven't given a detailed explanation so far. The deep dungeon Heaven on High was added in patch 4.35, alongside some triple triad cards. In patch 4.5 these cards were made obtainable by playing Triple Triad against Ushiogi. But in order to do that, players had to beat the quest "On the Shoulders of Giants", which is the unlock quest for Heaven on High floors 31 to 100 and requires beating floor 30 of Heaven on High. The equivalent quest for Eureka Orthos is "Rage Extinguished". If the Orthos triple triad card was just like the Heaven on High cards then in patch 6.5 completing the quest Rage Extinguished would unlock an NPC who we could play Triple Triad against to get the Gancanagh card. That has not happened. But as this explanation hopefully illustrates, even though the Heaven on High cards can be obtained by playing triple triad against an NPC, players do still need to engage with Heaven on High if they want those cards. If the equivalent conditions were applied to the Orthos card then players would still need to engage with Eureka Orthos, including by beating the monster represented on this card (the floor 10 boss)
You are almost certainly right that Beastmaster will have one or more cards locked behind it, but if they are anything like the Blue Mage ones getting those will simply require beating the Beastmaster quests and then buying those cards. Or beating the beastmaster quests and playing NPCs at triple triad to get them. Beating the relevant quests is a common unlock condition for getting cards out of triple triad NPCs, just not one that applies to the Gancanagh card.