In the video the graph is almost like the graph below:
Additionally I have drawn the objective function (blue line). To do this you have to solve the objective function, at level $C=0$, for $y$.
You need two points to draw it. One point is obviously $(0/0)$ and another point is for instance $(2/-3.2)$
Now you push the line right upwards parallel until the line touches the feasible region the first time.
The second picture shows the process.
The line touches the feasible region first at $(2.4/1.2)$. If you cannot identify the exact value from the graph you calculate the intersection of the two lines. Here they are the two constraints. But in many cases the intersection can be identified directly from the graph.
The more constraints a model has the more powerful is this method.
Is this an application of the Simplex Method ?
No, it is not an application of the Simplex Method.