Okay let's start at the very high level.

What Are Keiretsu?

Keiretsu are massive vertically and horizontally integrated Japanese business groups, each of which is consolidated around a private bank, some of which can trace their lineages back to the familial Zaibatsu of Meiji era Japan. The big six horizontal Keiretsu are DKB, Fuyo, Mitsubishi, Mitsui, Sanwa, and Sumitomo, although of those, Mitsubishi and Sumitomo, along with Mizuho Financial, are really the most powerful.

Then there are the newer vertical keiretsu, most of which deal in modern manufacturing like Honda and Hitachi and really grew out of the war or postwar era. Although 7&i Holdings (literally 7-11, as in the C-store chain) is also getting big enough to be counted among them (much like how Walmart and Amazon are the elephant in the room in the US).

So what about Sony?

Sony is reckoned among the vertical keiretsu. Like all their peers, they have a private bank, Sony Financial Group, which holds over 14 trillion yen in assets (almost half the total worth of Sony Group) and includes Sony Bank and Sony Life. SFG is somewhere around 10-20% of the total Sony Group revenues, so it's entirely possible that in some years, they could potentially be the leading component (ahead of the various individual entertainment and electronics companies in the group).

Where it gets even more complicated is that the horizontal keiretsu usually have their claws in the vertical ones, and are possessive of what's "theirs" even when they don't own enough to bring them into their group. Sony is effectively in the orbit of Sumitomo, while Nintendo is in the orbit of Mitsubishi, as is Square Enix.

Anyway, you would really have to go down deep into Sony group's financials to be sure, but it wouldn't surprise me if during the early loss-leader days of the PS3, that Sony Interactive Entertainment was probably not looking so hot compared to its peers in the group. But the whole point of the group being built around a central private bank is that they can do that sort of stuff without having to deal with activist investors complaining about the short term consequences to shareholder value. They can play the strategic long game.