Another way:
Module[{i = 0, l = #, f},
f[x_String] := Symbol[x <> ToString[++i]];
f[x_] := x;
Map[f, l, {2}]] &@list
{{0, x1, x2, 0}, {0, x3, x4, x5}, {0, x6, x7, x8}, {x9, x10, x11, x12},
{x13, x14, x15, x16}, {x17, x18, x19, x20}, {x21, x22, x23, x24},
{x25, x26, x27, x28}, {0, x29, x30, x31}}