I don't work in power systems, I work with low-voltage DC stuff, so when I think "the capacity of the battery system" I think it would mean the maximum stored energy.
But "The maximum amount that can be produced" is also a valid definition of capacity, and I'm guessing this definition might be used in power generation more often ("the generator is operating at half capacity").
If you're interested, the context is that capacity was historically used in the utilities industry to refer to generation capacity, which is in MW or GW. E.g., the capacity of a power plant could be 500 MW, which for the decades of power production preceding renewables, could be sustained indefinitely as long as you're feeding it fuel.
By extension, when you talk about battery capacity in the context of the electrical grid, you're talking about the MW or GW of generation that you can replace during peak loads. The ability to distribute batteries across a grid to meet peak demand (and defer infrastructure/peaker plant construction) is the best way (today) to justify investments in batteries.
And really, as you say, everybody talking about storage systems should be quoting both energy and power.
In this article, which is what we're discussing here, it is very clearly either a typo, or it's some journalist spouting off above their pay grade.
And if you're used to thinking about utilities, it makes a lot of sense, you think about power capacity, and then the duration afterwards. GW is a more direct way to approach that. If you want to get duration from GWh and GW, you have to do a mental division, which is slower than multiplication.
This is the best reason why they should quote both numbers: so we can be sure they haven't gotten confused and quoted energy as watts.
Currently, grid discussions happen mostly in the MW or GW space. Maximum instantaneous discharge speed is pretty much the most important characteristic for storage, up until very very recently, since it was mostly used for frequency regulation. Lately more and more articles are discussing total energy capacity instead, as this is discussed in wider circles than just those interested in the grid. Also note that the duration of discharge for a storage system is often implicit because it is deployed in an energy market where the bids are on fixed time periods (e.g. 4h).
Ideally we'd know both the GWh and the GW, but the collated stats have been mostly GW so far.
Guessing that they don't understand GWh vs. GW is pretty far off base. Though this may be a confusion of units that happens often in discussion with lay folk, it's not much of a concern when talking to people that are discussing the grid.