Yes there are other social forces today, but I think the point is that capital - not billionaires, monarchs, celebrities, or patriarchs - is in the driver's seat.

Arent all human institutions organised to maximize economic output in a given context?

All human institutions? That's a strong claim unless you have a very narrow definition of "human institution". Just like we agreed above - there are other social forces at play, and many of those have corresponding institutions. Any of them large enough to involve large amounts of people across larger regions usually have to be part of a capitalist world in many ways, i.e. raise funds or participate in a market or something, but that doesn't mean they're all organized to maximize economic output. Also, I'd count everything from big decentralized activist networks down to my little book club as human institutions, and many of those have no economic input or profit whatsoever.

When does it become capital instead of a the vast personal wealth of a roman patricisn.

The vast personal wealth of a Roman patrician doesn't circulate in a production economy and is far more fixed to the person/family than capital. Capital is not wealth but wealth with a kind of agency, ripping across the social and economic landscape corralling potential productive forces into it's sway. Capital can't just exist; it has to grow by continuing to circulate and pick up more exploited labour or it goes into crisis.

In a strange dark way capital is like life, a weird algorithmic quirk in a natural space that picks up speed and size through self-replication and mutation. Part of the problem is that the sheer causal power of large pools of capital that have tendrils all across the globe is way stronger than any individual or even individual nation-states, hence the calls for international proletarian solidarity and organization.

I don't know specifically about Rome, but in the patrician's case their wealth is likely more under their control to do with as they please. At the same time it probably comprises a wide array of different kinds of assets, many of which I would assume spend more time travelling vertically through heritage or other lineages than horizontally across the market.