I am not surprised that we would agree with a chess engine. If you are a solid player you have a good understanding of the logic of the moves, basic strategy (such as development, center control, piece strength, pins, forks, etc.), and some situations almost force moves when you have a good understanding of the game.
That's why I realized that I spoke too early, it's perfectly normal for certain amount of moves to be the same with a chess engine in the beginning of a game. Especially within a given opening it should be inevitable.
However except the unusual short games, after analysis of a full game(at least several games ideally and the more the better of course), if there are more than expect-able amount of moves that are same with what a modern chess engine would play, then that means there are just two possible explanations. Either the player is a very good chess player, or he/she gets help from a program. Of course, again, I'm not implying anything. It's just the fact that there is no way for a casual player to be able to play exactly the same or suspiciously similar to the modern chess engines such as Houdini, Stockfish, Rybka 3&4 or Komodo etc which are all well above 3000 elo ratings and can smoke any of the GMs of today in a match.
About the analysis part, it's a good indicator that if a player is consistently finding the best 3-4 moves throughout the game, an indicator of a very strong player/cheater, that is. Some game analyzers measure the frequency of the times that players pick those top moves. Another indicator would be the inconsistencies, like very unique and good moves in some parts of the game that betokens a comprehensive understanding of the game but some weak and unexpectedly bad moves in some other parts of the game(not to be mixed with blunders). Some chess engines can detect this inconsistencies pretty easily as well. One another indicator is the "hard to find" moves or move sequences. Chess engines will find them without a sweat, but it's nearly impossible for casual players to find them, even the great GMs would overlook them many times and they would be proud of themselves when they find them.
But at the end, you cannot tell if a player definitely cheats or not if you don't have enough gameplay data and if you don't consider the level of the player and the type of the game that is played. For instance, if Kasparov, Anand or Carlsen or some other top GMs were playing a game like we play here, their game analysis would show %99 of similarity with a 3000+ chess engine. Because they will have all the time to analyze their moves before play it which they are best at it. But If they were to play a regular lets say 2 hours of a chess game, they would play much less perfect game and differentiate in some parts of the game comparing to the chess engines that play almost perfect these days.