It's more like "social engineering" (targetting LLMs) than malware. A site that influences its (human) users to buy, vote, "invest" in scams and so on is malware?

I personally have a hard time considering it malware, because it's just instructions targeted at an LLM.

If someone put up a sign in a store that said "Burn this store down!" the person who put the sign up is not responsible if someone follows the instructions written on it, are they?

malware is a malicious program , it can be in memory even within another process but essentially its a little program of itself.

prompt injection is more close to an exploit. a sequence of input that leads to unexpected behavior, exploited to perform malicious behavior.

many exploits are hosted on websites. called exploit kits even. i think prompt injection match such classification. its very similar. a piece of data on the site's side exploits a program or interface on client side.

It's not malware. You chose to read their site.

Not sure it can be defined as malware if what it’s doing, if successful, is a net gain for humanity.