Use DataFrame.assign with DataFrame.explode for separate each word and then convert to dictionary:
d = df.assign(Title = df['Title'].str.split()).explode('Title').set_index('Title')['Category'].to_dict()
print (d)
{'Harry': 'Fiction', 'Potter': 'Fiction', 'and': 'Fiction', 'the': 'Fiction', "Sorcerer's": 'Fiction', 'Stone': 'Fiction',
'The': 'Sci-Fi', 'Matrix': 'Sci-Fi', 'Movie': 'Sci-Fi', 'series': 'Sci-Fi',
'Diary': 'Comics', 'of': 'Comics', 'a': 'Comics', 'Wimpy': 'Comics', 'Kid': 'Comics'}
Or use dict comprehension:
d = {x:b for a, b in zip(df['Title'], df['Category']) for x in a.split()}
print (d)
{'Harry': 'Fiction', 'Potter': 'Fiction', 'and': 'Fiction', 'the': 'Fiction', "Sorcerer's": 'Fiction', 'Stone': 'Fiction',
'The': 'Sci-Fi', 'Matrix': 'Sci-Fi', 'Movie': 'Sci-Fi', 'series': 'Sci-Fi',
'Diary': 'Comics', 'of': 'Comics', 'a': 'Comics', 'Wimpy': 'Comics', 'Kid': 'Comics'}
EDIT:
First each dictionary has unique key, so by default are duplicated values lost or processing some aggragation - here is used join:
print (df)
Title Category
0 Harry Potter and the Sorcerer's Stone Fiction
1 The Matrix Movie series Sci-Fi
2 Diary of a Wimpy Kid Comics
3 Diary of a Kid Sci-Fi
d1 = df.assign(Title = df['Title'].str.split()).explode('Title').groupby('Title', sort=False)['Category'].agg(', '.join).to_dict()
print (d1)
{'Harry': 'Fiction', 'Potter': 'Fiction', 'and': 'Fiction', 'the': 'Fiction', "Sorcerer's": 'Fiction', 'Stone': 'Fiction',
'The': 'Sci-Fi', 'Matrix': 'Sci-Fi', 'Movie': 'Sci-Fi', 'series': 'Sci-Fi',
'Diary': 'Comics, Sci-Fi', 'of': 'Comics, Sci-Fi', 'a': 'Comics, Sci-Fi',
'Wimpy': 'Comics',
'Kid': 'Comics, Sci-Fi'}
For compare:
d = df.assign(Title = df['Title'].str.split()).explode('Title').set_index('Title')['Category'].to_dict()
print (d)
{'Harry': 'Fiction', 'Potter': 'Fiction', 'and': 'Fiction', 'the': 'Fiction', "Sorcerer's": 'Fiction', 'Stone': 'Fiction',
'The': 'Sci-Fi', 'Matrix': 'Sci-Fi', 'Movie': 'Sci-Fi', 'series': 'Sci-Fi', 'Diary': 'Sci-Fi', 'of': 'Sci-Fi', 'a': 'Sci-Fi',
'Wimpy': 'Comics',
'Kid': 'Sci-Fi'}
d = {x:b for a, b in zip(df['Title'], df['Category']) for x in a.split()}
print (d)
{'Harry': 'Fiction', 'Potter': 'Fiction', 'and': 'Fiction', 'the': 'Fiction', "Sorcerer's": 'Fiction', 'Stone': 'Fiction',
'The': 'Sci-Fi', 'Matrix': 'Sci-Fi', 'Movie': 'Sci-Fi', 'series': 'Sci-Fi', 'Diary': 'Sci-Fi', 'of': 'Sci-Fi', 'a': 'Sci-Fi',
'Wimpy': 'Comics',
'Kid': 'Sci-Fi'}