There are no batteries involved with the type of solar pumps the article is talking about. They are likely 3 phase pumps powered by variable frequency inverters. The inverters are similar to the VFD¹ motor drives commonly used with industrial machines.
I'm not sure where you came up with a $20,000 cost estimate but it's likely a lot less than that. Particularly if you buy the cheapest stuff direct from China, avoiding avoid the dealers/installers who are probably marking up the equipment by more than 100%. Solar panels and the associated electronics have drastically dropped in price for the past several years. It should be possible to get 200 watt panels for $50-100 (or maybe even less if you buy a lot of them) That's something like $250-$500 per kW of panels. Make it $1000/kW to cover mounting hardware and wiring. The pumps / inverters are maybe a few thousand for a fairly large system.
I'd say the total should come closer to $5,000-$7,000 per acre based on the power requirements you specified.
[1]. https://en.wikipedia.org/wiki/Variable-frequency_drive