No, it does not beg the question, because the question Spolsky is answering is practical, not epistemological. He's describing the best, simplest structure for equity allocation. He didn't give you a magic calculator.
Well, you know, you're working in the kitchen and I'm waiting tables. Last night's tips were $100 and I have a perfectly fair system for dividing them. I get $50, here's $40 for you, and I'll give $10 to the busboy. Or maybe it's $80 for me, $20 for you, and screw the busboy. It doesn't really matter as long as everyone agrees and it makes sense. But my system is really fair, you know.
This would be wittier if dividing tips was anything at all like allocating equity; in reality, the only thing the two problems share is arithmetic operators.
Blunt contradiction does not really make an argument. If you had something more precise to say than "give less equity to people who joined later" - now that would be interesting.