Bug is a kid’s term for bug-like things. That’s as closest to a scientific definition you’ll get. It’s like trying to precisely define creepy-crawlies.
Case in point: the children’s movie A bug’s life. There’s a spider and two rolie-polies in the main cast, along insects (not sure all are in the Hemiptera clade).
Do you think this person had that response all planned out ahead of time? Is that why they posted the first thing, so they could catch someone with the second?
Even if you give him missing the joke. Bug as used colloquially refers to spiders and insects, not just true bugs. There is a reason why true bugs have to be called true bugs.
The Hemiptera are called 'true' bugs because everyone - entomologists included - tend to call all insects 'bugs'. That is a loose term, whereas the true bugs are just those contained within the insect order Hemiptera.
He'd only be missing the joke if the spider's preferred beer was True Bug Lite.