I know you said profit...
Then why are you talking about anything else? Valve and Nintendo, although operating in a similar market are vastly different companies. One area where they do overlap is the digital distribution of games, so let's take a look at that shall we?
First of all, let's start with Steam. Valve are quite cagey on sales/revenue and being a private company, they are under no obligation to reveal exact sales figures/revenue/profit details (I would be very interested to read the article/press release that you site claiming that "in Valve's best year (2014) their revenue was 1.5 billion, please post a link), but Steam Spy puts the figure for 2015 at $3.5 billion.
http://gearnuke.com/steam-sales-2015-valve-generated-total-3-5-billion-paid-games/Now let's take a look at Nintendo with regards to online distribution. according to this article from Nintendo Life, it states that in 2015 the Nintendo eshop generated a revenue of just over 3 Billion yen, or or $270 million
http://www.nintendolife.com/news/2016/04/nintendos_eshop_revenues_hit_a_new_high_driven_by_dlc_and_generation_i_pokemonThe article also states that 2016 was Nintendo's best year for online distribution but I don't have the Steam numbers for comparison.
So, going by 2015's numbers we have:
Steam revenue: $3.5 Billion
eShop revenue: $0.27 Billion
Also worth noticing is that some months on Steam eclipse the entire year of eShop. Also, GTA V alone accumulated half the revenue of the entire eShop.
As far as Sony and Microsoft are concerned, it's still not very comparable.
I'll just leave this little doozy here for anyone who may have forgot, courtesy of Eurogamer and many other outlets:
http://www.eurogamer.net/articles/2016-04-28-sonys-psn-is-making-more-money-than-all-of-nintendoNintendo is a truly huge company and their revenue will reflect that, but good business management is what dictates profit... or lack thereof in Nintendo's case.