I was not sure about just mentioning a random company name here but I'm really at a loss with this and probably missing something.

If an alternative meaning to 任天堂 is the temple of free hanafuda, . . .

. . . I do not see where 'hanafuda' is, and every explanation does a great job of leaving it out. Or, they see it as important to explain to you the relatively obvious 任 and 堂 but not where hanafuda is coming from. I mean it literally looks like they left hanafuda to 天.

Nintendo
https://www.facebook.com/Nintendo.hk

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A blog on Asian go books, go sightings, and interesting tidbits
Go is such a beautiful game.

They say that the meaning of nintendo the founder intended is to put fate in heaven's hands. And that makes sense when you're playing 100-peom karuta

But I don't see what people mean when they say he might have meant the temple of free hanafuda according only to those three kanji characters!

No-one actually knows the meaning of Nintendo, but there are likely several layers of puns. Every card company had logos that were printed on each pack. and Nintendo used the image of a Tengu, a long nosed goblin. A nose in Japanese is hana, a homonym for hana=flower. Flower cards (hanafuda), derived from older hana-awase cards, were used as substitutes for kabu cards, to avoid excise duty or gambling restrictions, and hana became a code word for gambling (and rubbing the nose became a way of asking where one could play). So here ten = hana. Nin is probably from a yakuza word for chivalry - they see themselves as knights (the ninkyo dantai) who don't exactly rescue fair maidens in distress but who, for a fee, will gladly duff up a stroppy neighbour or recalcitrant borrower if you go down to the local yakuza shop and hire their services. But when such custom is slow, of course the yakuza will do other things such as gambling and pimping. To cover their tracks they make great use of code words, such as words pronounced (syllabically) backwards, in much the same way an East End gangster in London might offer to do a job for you for "a monkey for cash". (This comes to mind because the star of Minder died this week.)

'Do' does not mean temple here. It's just a grandiose word for a shop. A n emporium.

The games the yakuza played with hanafuda were nothing like the children's games of koi koi and so on. They were more like blackjack. The suits just represented numbers (pine - 1 , plum -= 2 and so on), and a hand that scored 0 (modulo 10) was the worst possible (and 9 the best), and was the result of three cards 8 + 9 + 3 (i.e. ya + ku + sa=za). So the legend goes.

Thank you very much, this is just what I was looking for!