nice one.
It is caused because you invoke the rect before size().


Explanation
Before the usage of size() width and height are 0.
When you make your object this is before size, thus
width and height are 0:

1. Drunkrect w = new Drunkrect();

You use width and height in the constructor which is called by new.


solution

1. class Drunkrect {
2.   int x;
3.   int y;
4.   Drunkrect () {
5.     x = width / 2;
6.     y = height / 2;
7.   }
8.   void display() {
9.     fill (0);
10.     rect (x, y, 11, 11);
11.   }
12.   void step() {
13.     int choice = int (random (4));
14.     if (choice == 0) {
15.       x++;
16.     }
17.     else if (choice == 1) {
18.       x--;
19.     }
20.     else if (choice == 2) {
21.       y++;
22.     }
23.     else if (choice == 3) {
24.       y--;
25.     }
26.   }
27. }
28. // ==================================================
29. Drunkrect w;
30. void setup () {
31.   size (800, 800);
32.   w = new Drunkrect();
33.   // frameRate(1);
34.   // background (255);
35. }
36. void draw () {
37.   // background (255);
38.   w.display();
39.   w.step();
40. }