You can also get your points simply via points:
The points attribute contains a list of tuples containing an (x,y) coordinate for each point in the shape.
import shapefile
shape = shapefile.Reader("C:/TempData/test/grids.shp")
feature = shape.shapeRecords()[0]
points = feature.shape.points
print(points)
That results in
[(413795.5781, 5655831.7174), (413895.5781, 5655831.7174), (413895.5781, 5655731.7174), (413795.5781, 5655731.7174), (413795.5781, 5655831.7174)]
Also with this method one can refer to a specific point of a feature:
point2 = feature.shape.points[2] # vertex #2
print(point2)
will give you
(413895.5781, 5655731.7174)