I believe your link is accurate for what you asked. I have had my State's grant page open all this time, to monitor the refreshes, availability and distribution of funds by type of grant, which town and/or county, and also I keep scanning the individuals and businesses listed for their amounts. I understand this as, they got taxable income to use on specific expenses, so that will be a wash for them. It's not the same as EIDL or PPP. For examples, a health professional partnership got funds towards their additional costs for PPE; a theater got the funds towards lost revenue to prevent loss of the building and to cover ongoing costs as a bridge to reopening. The county distributed the allocations from the State, which got the Federal funds.

"This financial assistance was funded through $1.25 billion in federal emergency relief funding through the Coronavirus Aid, Relief, and Economic Security (CARES) Act. The receipt of a government grant by a business generally is not excluded from the business's gross income under the [IRS] Code and therefore is taxable. More information is available here."

And that link from my State's website is the same one you already provided 🙂