How are all LTI systems also dynamical systems? I understand that LTI systems are linear and time invariant and that dynamical systems describe how one state develops into another, but how would this make all LTI systems dynamical systems?
Dynamical Systems are any systems that change with time. Real physical systems or system models. What is changing? Any variable within the system (examples, displacement, velocity, pH, sound intensity ...). They can be linear, nonlinear time varying or not, etc. So it's a very broad definition.
LTI systems are a subset of dynamical systems that are strictly linear and the parameters do not change with time. They are usually models of real systems. Real physical systems, if you look close enough are never linear. Parameters can change with temperature for example. So LTI 'models' better suited. They approximate dynamic systems that are near linear and time invariant.