19x19 is the normal go board size, I've never heard of anyone playing on a bigger board. Computer players for smaller boards (13x13 and 9x9) have been very good for a while, it's a much easier game on this smaller boards.
I think the parent's point was about whether the AlphaGo AI can generalize to a different board size (as a human player presumably can) rather than about what is the normal Go board size, or what board sizes are easier or harder.
The parent was suggesting that while a human might possess a general understanding of Go, performing comparably regardless of board size ("The human would play on the same level"), the AlphaGo AI in contrast might drop significantly in capability on a board of different size. In effect, the AlphaGo AI might just be a very well-fitted (perhaps even overfitted) machine-learned algorithm on a 19x19 board, lacking a fundamental "understanding" of the game that could generalize to a different board size.
