1) If retained corporate earnings were treated as taxable income to shareholders, yes, there should be a credit on the capital-gains tax, or a basis adjustment, to reflect that fact. In the first example, the woman's basis, which starts out at zero, should be increased to $60,000 (assuming she pays the tax on the $60,000 from noncorporate funds). Therefore, she would owe no capital-gains tax. But if she sells the stock for more than $60,000, she owes tax on the difference. Why not? It's income. Ditto the second example.
2) Even where losses and gains are exactly equal (e.g., your costless casino), there are individual winners and losers, so I do not follow your argument that if a situation produces no net tax revenue it should be exempt from taxation. Why shouldn't the lucky winners pay a bit more tax and the unlucky losers a bit less? The real-life asymmetrical tax treatment of gambling is a noneconomic policy decision I have mixed feelings about.
3) You concede that in the stock market, by contrast, real gains exceed real losses. Yet you also concede that if losses were deductible without limit (and the limits are much less onerous than on gambling losses), net revenue to the government would be zero. That, John, is precisely why it's reasonable to have limits! See my earlier detailed explanations of all this.
4) Without settling whether taxes on capital are "ultimately" paid by labor (if so, it's odd that holders of capital--such as the backers of your center--raise such a fuss about them), I merely note that the tax on labor is directly paid by labor. For any given level of income-tax revenue, less raised from capital means more must be raised from labor. The point is not to punish or burden either capital or labor, but to raise the necessary revenue as fairly and efficiently as possible.