That is a very rapid and instantaneous motion indeed.
Yes MSFS is a "simulator" - game. Its main selling point is visual reproduction on a PC screen of aircraft instrumentation and out-of-the-window views, and it can help in learning what aircraft systems there are and how to operate them. But how exactly the instruments respond is of secondary concern.
In contrast to this is a Level D Full Flight Simulator, which must demonstrate to aviation authorities that simulated aircraft dynamics are within tight tolerances of flight test data from the aircraft. For instance the sideslip angle response to a pedal input with both Yaw Damper ON and Yaw Damper OFF.
Responses above would be for a Level D sim of a subsonic passenger jet with gear UP, yaw damper OFF, at 10,000 ft and about 160 kts.
- The pedal is deflected to about 1.5° in 2 seconds - a finite time, there is damping in the pedal feel, plus an opposing force.
- The rudder deflects much in unity with the pedal, actuated by the hydraulic system.
- As a result of the rudder deflection, sideslip angle enters a second order response with inertia and damping effects.
Peak value of $\beta$ = 2.4° is reached after 6 seconds, which is indeed not what we see in the video. Plus the response is an acceleration, as can be seen from the gradual increase of $\beta$ starting from zero until a constant yaw rate is reached.
So is the rapid and instantaneous MSFS response realistic? Not really, no. It looks like a rudder deflection equates to an immediate yaw rate, there is room for improvement.