Read csv file, parse data, and store in a dictionary

[DeaD_EyE]

If you're sure, that you have only 3 columns everywhere, you can use item unpacking.

with open('playlist.txt', 'r') as csv_file:
    playlist_dict = {}
    reader = csv.reader(
        csv_file, quotechar='"', delimiter=',',
        quoting=csv.QUOTE_ALL, skipinitialspace=True
    )
    for timestamp, song, artist in reader:
       dt = datetime.strptime(timestamp, '%B %d, %Y %I:%M %p')
       playlist_dict[dt].append((song, artist))


print(playlist_dict)

You can make it shorter.
No use of splitlines, because the csv_reader does it indirect.

I corrected the assignment in #11 of your code.

If you want to assign a value to a key, it looks like this:

some_dict = {}
a_key = 'my_key'
some_value = 42
some_value = (1,2,3) # could be a tuple
some_value = [1,2,3] # could be a list
some_value = {'foo': 'bar'} # or  a dict
some_value = {1,2,3} # could be a set

# assignment 
some_dict[a_key] = some_value # in this case the name was last overwritten by a set

Keys could be only hashable objects. This means you could not use mutable mappings/sequences as key.
The datetime object is for example immutable. The values of a dict, don't need to be hashable.

And since Python 3.6 we've got the implementation detail, that dicts keeps the order.
Since Python 3.7 it's in the language specification and a guarantee.

If you test your code with older Python version, you'll get scrambled results.
Previously dicts didn't keep the order. In some versions they used an algorithm to scramble it.

If you want to write code for older Python versions, you have to know it.
In this case you can use collections.OrderedDict.