I remember reading something from awhile ago that more than a few people don't use the editor to actually write their storygames as of incidents where something happened and the nice, hearty page they just wrote did not save and got wiped when closing. It has happened to me more than once. People like these tend to use other programs or use sites that do these things anyways for the actually writing of their storygames. For these people, it won't be seen as worth the effort.
It also won't be seen as worth the effort by people tend to know their grammar and/or have other people read over to check anyways.
It won't really help improve grammar in storygames, unless you are really clueless about grammar or you drunkenly write something uncomhensible and then check it later. Grammar mistakes that stay in a work are because of ignorance, not caring enough to fix, or they are there on purpose.
Most people who write things worth reading should have at least some understanding of grammar. Grammar is something one should have a understanding of if one intends to write. If you drive a car, then you should have some idea of the rules of driving a car. It is the same thing really. Responsible writers that are writing seriously should not write without understanding the rules of writing which include grammar, spelling, character development, and other such things.