1. Even if the Dodgers hadn’t saved/invested one penny towards those future obligations, and even with his potential legal troubles and other financial issues, Walter could cut still easily a personal check today that would cover the nominal value of all future obligations (without any discount for present value). Yes, he is that rich.
2. Where I disagree with your comment (“when a big portion of your payroll is going to guys that played for your 15 years ago, you won't be able to outspend your competition”) is that you are thinking of those future obligations as part of the 2036 or 2045 or whatever year’s payroll. They’re not.
Unless the Dodgers are run by complete morons, they’ll have long since allocated money and invested it so that (as Edgy noted above) it will have already covered those future obligations and then some. The then-current payroll will be a totally different pot of money.