How to read this formula for win chance probability?

You are simply missing two parentheses

I get $\frac{1}{1+2.71828^{-2.012(5.5-5.3)}}=0.599\,26$ while you calculated $\frac{1}{1}+2.71828^{-2.012}\ast (5.5-5.3)= 1.\, 026\,7$.

Since $e^{-2.012 * (5.5 - 5.3)} > 0$, you should have that $1+e^{-2.012 * (5.5 - 5.3)} > 1$, and hence $\frac{1}{1+e^{-2.012 * (5.5 - 5.3)}}<1$ .. so something is indeed off.

Now, you write that you calculated

$1 / 1 + e^{-2.012 * (5.5 - 5.3)}$

I wonder if you forgot some parentheses there, i.e. maybe you ended up calculating

$(1/1) + e^{-2.012 * (5.5 - 5.3)}$

rather than:

$1 /( 1 + e^{-2.012 * (5.5 - 5.3)})$

or something like that?

Anyway, the formula clearly should get you a value between $0$ and $1$, so nothing's wrong with the formula. It's something with how you calculated it.