In all the previous situations in the game the parser limited itself to two word commands, which caused me to think this was all it could understand.
No, such limit does not exists. It recognices two word clasic inputs, but you can try plain english in all the game, as a gentleman would do! :D
It gave that impression though, but that could simply due to how it handles words it doesn't understand. (for example, any sentence that contains the word left is treated as a command to walk left)
Not exactly that way: In the top of the first tree, you can "Look to the left" or "Go left", each one doing different actions.
Poor Gent Stickman tries to understand you the best he can with his open head, using what is known as loose parsing mode, versus strict parsing mode that would be more suitable for learning languages games, for example, to check correct gramar.
Thanks for playing! ;)