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ANSWER: Yes, it is possible for your grandchild to qualify for the benefits, so long as the child is considered a "dependent" and has lived with her grandfather for a specific amount of time.
To be dependent your grandchild must have begun living with her grandfather before she turned 18 years old, in the US, and received at least one-half support from her grandfather for at least one year prior to the month her grandfather became entitled to retirement or disability insurance benefits or died.
That is the simplest explanation. There may be another path, if this does not apply in this case, but based on what you've told me, I think this applies.
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