According to user Lorean at Steam Community:
A quite late response, but I keep a spreadsheet to track my achievements and I just tested this. with some functions. Dividing completed achievements vs total achievements gives me 40%. Calculating the average of each individual game's achievement completion % gives a result of 52.11% which would match with my profile's average completion rate of 52%.
And furthermore, to answer your question. User Canti in the same thread:
Games that have no achievements are not factored in at all.
Likewise, games you have not earned any achievements in are also not counted. Only when you get 1 achievement will the game start to count it towards your average.
So games without any completed achievements do not count towards the Avg. Game Completion Rate.
More examples are given in the same thread. Here is user Boys Dont Cry:
I can confirm it's the average completion of all games played with achievements.
Games with 0 ach. doesn't count
But F2P and demo not any longer available like Call of Duty: Black Ops - Multier (I got 2 out of 3) is included in the total and the completion Rate
For games there I have at least 1 achievement:
I have 1428 of max 2270 => 63%
but average of percentage for each game => 68% same as on my profile page