Yes I can. I cannot force you to acknowledge my ownership, but I also can't force you to acknowledge my ownership of my wallet, or my computer. Just because it is easier to steal the former doesn't make it any less of a theft.
No you can't. Any abstract idea can be represented by a number and numbers just inherently exist.
Both of your premises are false, though I assume your first premise is intended to read "All abstract ideas that could be offered for sale/consumption can be represented by numbers," which is possibly true but I think still stretching reality. I mean, good luck converting, say, Maria Abramovic's art into numbers.
Numbers may inherently exist, but specific numbers do not. A 3-minute piece of music on CD is about 3 MB, or 24 Mbit. (But sheet music! No, lots of music can't be properly notated at sheet music.) The number of numbers that long is 2^24000000. The creator picked one of those numbers, and it wasn't at random. Sure, you can't own the number, but you sure as hell can own the algorithm for determining the number.
Separately, I have a ton of ideas which I own solely because they are still in my head. Good luck getting those for free.
and something that you can infinitely duplicate shouldn't have any value.
Says who? Who let you dictate societal norms and laws? Ideas and words have value.
The law of supply and demand.
This may come as a shock, but the law of supply and demand is not the end of economics or of society.
I would pay for the time they spend working on the game, but most game developers choose to do that for free instead.
No they don't. Most game developers get paid in some fashion. They require food and shelter just like you do.
The people who work for a company that develops games might get paid for their time by the company, but it's super rare for the company to get paid for that by the customers. Instead, the company gets paid for merchandise (e.g. game DVD ROMs) which is also understandable because the physical merch does have value too, and digital copies of the game, which is ridiculous.
Tell that to Notch. Or one of the hundreds of game designers out there for whom the company is (or was) synonymous with the designer(s).
It's worth noting that you can legally download my band's music for free and you can create whatever derivative works you want as long as those derivative works are released under the same license. While I want to do this just out of principle as well, I also think that it's the best strategy if we want to succeed as professional musicians because having people listen to our music for free is vastly preferable to having people not listen to our music at all.
And that's admirable, great! But not every musician/filmmaker/author should be forced to follow that model.
Mostly, intellectual property laws just serve to further benefit the record labels and artists who don't have any real financial issues to begin with, at the cost of artists who are just starting out.
Again, tell that to independent authors/musicians/filmmakers/artists who rely on intellectual property protections.