As per the article, the plant that tripped was in another state, Victoria, 600 miles away (+) from the battery. Energy USUALLY flows from Victoria to South Australia
The unit that they blamed for slow response was two states further away, an additional 1,000 miles.
So being middle of the night, there would have been a connected grid of 15,000MW of supply/demand, and I'm not sure that LY3 was likely at full load at that time of the night...looks like they used "available" capacity...in fact I'm sure...the Units are rated at 52MW, and registered at greater.
Anyway, 560 (if it was that, and it wasn't) was about 5% of the grid at the time...8MW injected in SA was 0.05%, so consider how it contributed.
At the time, there would have been 20 or there abouts thermal units running, with 200 tonnes per unit spinning at 3,000RPM...that's what they refer to as Inertia in the grid, 4,000 tonnes of spinning metal...decelerating them means that they pump more into the grid immediately, before their governor kicks in virtually instantaneously...that's the 6 second response that they refer to...then there's 60 second and 6 minute contracts that had to be met.
When frequency drops, every motor driven load on the grid drops load as well, as it's operating speed has dropped also...burns out fridge motors ultimately.
So nope, it did little to nothing...but we have no ideas of the secret contracts, nor payments that South Oz is grandstanding about after they blacked out the other year.
The guys who model the markets are concerned at how these things work, as they have no inertia, and claim that they can respond in 1/3 of a cycle...the real risk is that they respond en masse (when there's enough of them), and the grid oscillated uncontrollably.
Not buggy whip fears, just usual cart horse inversion by idealogues, who like the author in the link use facts loosely to create a sensational argument that's factually iffy.