I've ran stockfish through the entire game for black only. For each move he had 5 seconds to think (thus around 5 minutes total, same as the OP said Houdini had to think). Brief results:
21. Qc8?! (suggested Ne5). Difference: 0.57
31. Bd8?! (suggested Ra4). Difference: 0.81
43. Kf7?! (suggested Bb6). Difference: 0.53
44. Ke7?! (suggested e4). Difference: 1.30
48. Bf4? (suggested d3). Difference: 2.86
54. Ke5? (suggested Kc5). Difference : 1.76
Houdini blundered really hard, especially at the end. 2.86 in particular is just too much. A variation stockfish suggested on the 48th move:
This is a huge difference with the moves that were actually played.
Of course this analysis only took 5 minutes and was only for black, it is very likely that at least one of the following may be assumed:
1. Houdini suffered greatly from limited time (especially at the end).
2. The hardware on which houdini was run lacked.
3. Houdini was not playing on full strength.
My conclusion: I will not speak about your nephew's skill in chess, but implying that Houdini was beated by your nephew is misleading. Houdini was handicapped, in one or more ways.
Here are results of a quick analysis of that game, using Houdini 1.5a, 512MB hash, 10s/move, at least 14 plies, analysis starting from move 26 (per pfren's diagnosis of 25 book moves). CPU: 2.66 GHz i7, single processor used.
For those unfamiliar with top-3 methodology for detecting engine use, top-1 is the percentage of positions where the 1st egine choice was played, top-2 is the percentage of positions where either the 1st or 2nd engine choice was played, et.c.
Adam Top1 match: 24/36 = 66.67 %
Adam Top2 match: 33/36 = 91.67 %
Adam Top3 match: 35/36 = 97.22 %
The 10s/move analysis time was based on the OP's statement of having given Houdini 5 minutes for the entire game. This setting is not really correct, but not much can be done without knowing the exact time that the opponents took for each move. I have only the free version of Houdini, so that's another source of inaccuracy.
Given the inaccuracies and small sample, there's no way to draw firm conclusions, however, the numbers are consistent with what might be expected from analyzing a Houdini-Houdini match.