It's effectively a grant. The US government isn't buying existing shares. Intel is issuing new shares and selling them to the US government - so actual money is being transferred to Intel (and existing shares are being diluted as a result).
That's just buying stocks (at-the-market offering).
Nope.
When I buy stocks at market price, the company gets none of my money.
When the company issues new stocks and sells them, the company gets the money.
I think you're maybe unfamiliar with what an ATM offering is; try googling it.
Fair point. The key issue in the thread, which I think we both agree on, is that yes, the government is giving money to Intel.