The result is an interpolation function. So there is no "data points". You can use the function to generate the points you want. Interpolation function can be used as any other function. You can differentiate it, integrate it, plot it , etc...

ClearAll[x,t]
eq = x'[t] == (1/4) x[t - 15]/(1 + x[t - 15]^10) - x[t]/10;
sols = First@NDSolve[{eq, x[t /; t <= 0] == 0.01}, x, {t, 0, 10}];
x[1] /. sols 
   (*0.0114274*)

So you can Table command to generate points as needed.

    Table[{i, x[i] /. sols}, {i, 0, 10, 1}]
(*{{0, 0.01}, {1, 0.0114274}, {2, 0.012719}, {3, 0.0138877}, {4, 0.0149452}, {5,0.015902}, {6, 0.0167678}, {7, 0.0175512}, {8, 0.0182601}, {9,0.0189015}, {10, 0.0194818}}*)