Do we have profit numbers, for instance Nintendo made $1.55 billion profit.

How you figure?

9 months FY

Sony operating income - 247.2 billion yen
Nintendo operating profit - 220.029 billion yen

But they would have received it. When somebody buys say COD on PSN it doesn't matter that Sony only keep what 30%? of the amount, the full price would still be paid to Sony and go through their bank before being paid onto Activision.

I think they do count the entire $60 as their revenue. However, I would not say it's exactly the same.

You're familiar with the term "shipped units" I presume? That's what publishers/distributors have sold to retailers like Gamestop.

Generally speaking, if let's say Capcom has shipped Resident Evil 2, it's almost as good as a sale to them, and they don't necessarily care what happens after that, whether it sits on the shelf of the retailer forever, or reaches the hands of a buyer. They still got their money. Of course there are other reasons for why sold through units are more important, such as the potential extra sale of DLC and microtransactions, etc. But they don't have to wait for the game to get sold (again) for them to present those shipment figures to their investors.

That's not the case for a retailer like Gamestop though. In order for them to make money on that transaction, they're reliant on the product being sold through to the customer as well.
In other words, Capcom's "cut" for Resident Evil 2 is already taken care of during the initial transaction when the games are "shipped" to Gamestop.
It's basically the price at which Capcom chose to sell the game to Gamestop for.

So when Gamestop sell Resident Evil 2 for $60 to a customer, that's all Gamestop's revenue. Capcom don't take a piece of that sale literally speaking. They already got paid before the sale.
Then the profit for Gamestop is calculated after you take all the revenue and subtract all the expenses, such as the cost of buying the game.
So basically, because Capcom already got paid when the games were shipped, whatever Gamestop make on the transaction when selling to a customer is theirs to keep.

However, that's not the case when selling games through a service like PSN. Because they don't buy in any quantity of games, Capcom only get paid after the game has been sold to a customer. So everything Sony got from that sale, isn't theirs to keep.

The $60 that Gamestop gets is all theirs. But the $60 that Sony gets is not all theirs. Which makes me a bit unsure if they count all of it as their revenue. Since its electronic, Capcom could technically get their cut immediately upon every individual sale. Though I doubt that's the case. Rather, I think Sony hold the entire sum initially, and then pays the publisher on a regular (maybe monthly) basis based on the number of copies sold and at which price it was sold.

They do earn or receive it though. You buy a $60 game from PSN and Sony receive $60, that's a fact. It doesn't matter that they have to pay out $40 (or whatever the actual amount is) to the publisher of the game after that, they still initially received $60.

I get that you see it that way, but it's not legally revenue when the money goes through them to be filtered off to another company. Steam's revenue reports are theirs and do not include the money that developers get. 

Think of it this way.

If they did it your way imagine how shit their profit margins in their reports would be if their earnings report showed they LOST $40 for every 3rd party game they sold. That's 100's of millions of loss every single quarter. That doesn't look good, and it's obvious that's not the way they do things. 

No, because that $40 per game loss would be offset by the $60 dollars they bring in, leaving the profit (well, you still need to take off marketing / server costs / employee salaries etc.)

I own part of a small graphics design business - we sell printing to our clients, though we don't actually print anything ourselves, we outsource. The total money we receive from clients over the year is our revenue or turnover, the amount left after we take off what we've paid the printers plus our other costs & overheads is our profit.

In this instance we're the PSN equivalent and the printers are the 3rd party devs.

How is that not legally revenue? When I go to a restaurant and buy a $10 meal they record that as $10 in revenue. If they were to deduct the cost of the food from that and then report the reduced amount as revenue then that is what would be illegal.

Also that $40 is not a loss, it's an expense All businesses that sell products have the money they pay to the producer of said product as an expense. It would show $60 revenue, $40 expense & $20 profit for each 3rd party game sold.That's not accounting for other expenses of course, but that's the jist of how it would work.

Besides how else would their revenue be nearly ¥1.4T while their profit is ¥247.2B*. There's a ¥1.15T difference between those figures, if payments to 3rd party publishers for their games purchased through PSN doesn't count as part of that money then what on earth did they spend ¥1.15T on?

*profit figure taken from Rol's post is Apr-Dec rather than the full year like the revenue figure in OP, but even including Jan-Mar profit there would still be a huge disparity between revenue and profit so the point still stands.