Parentheses after Typing Environment
$\Gamma$ here is overloaded notation. The meaning of the expression $\Gamma(x) = \tau$ above the inference line here is given under the "Type rules." section of A Short Introduction to Systems F and F Omega on page 5. In this setting, $\Gamma$ is an inductively-defined function sending variables (in $\Gamma$ considered as a context, i.e. a list of variables) to their types.

A more illustrative, syntactic way to write the rule you give might be: $\frac{}{\Gamma,\ x : \tau\ \vdash x : \tau}$, where $\Gamma$ ranges freely over contexts. Note that the order of variables in a context here does not matter, so this rule allows us to project any variable in a context as a term.