They absolutely have something to divide, the current equity. You are working against your own interest by helping to add value to the company without setting your option price and share count. If the 100% owner isn't willing to share now, something is wrong. There are a number of ways to address the issue of actual performance: time based vesting, milestone completion vesting, a cliff for a probationary period with no vesting (typically 6-12 months and then the 6-12 months all drop in). This is a very serious red flag if they have incorporated and tell you "they don't have something to divide." It's much better to have the disagreements now (and perhaps let some folks go along the way for poor performance) than effectively make it a competitive free for all on an ongoing basis (can you imagine the discussion in 6-12 months "I did more than you" "No I did a lot more than you, and I spent most of my time fixing your mistakes"). You are right to worry about team dynamics.
The company has a strong team, a strong product, and market traction. The equity argument is as much about risk as it is about effort, and it looks like everyone else on the team has borne far more of that than our friend here. He's an employee, not a founder; his code contribution likely does not entitle him to demand equity reallocation.