I wondered how long it would take for someone to bring up VAT - your analogy is a fallacy because VAT is not charged/sold in isolation. You don't choose to buy VAT - you choose to buy an item that may be subject to VAT.
For this analogy to be valid, gambling would have to be an additional mandatory option taken when you bought another item. Buy a toy and be forced to buy a lottery ticket with it for example. The choice element being, do I buy a toy or not. But you aren't forced to buy gambling with a toy, because it isn't a tax. It is entirely optional REGARDLESS of what other items you buy. You could literally buy millions of items and STILL not have to pay for gambling. Whereas you would have to pay the VAT on the items it was applicable to.
To put it another way, VAT is a by-product of the purchase of another item. Gambling isn't. You are explicitly choosing to spend money on gambling. A direct affiliation. VAT on the other hand is an indirect affiliation based on your decision to buy something else. Some people might not even know whether they are paying for VAT or not when they buy an item.
If you chose to buy no items at all with VAT on them, that wouldn't mean VAT isn't a tax, because it would still be mandatory for others who did buy items with VAT. The applicability of VAT isn't impacted by whether you personally do or don't buy anything.
Going back to my earlier point, if we go down this path that it is a tax because if you choose to pay for it, you have to pay for it, then effectively that infers that everything you choose to pay money for is tax (it isn't).