Return to Answer

-- window functions
SELECT 
    -- m.*,
    movie_title, start_date_time,
    price, quantity,

    SUM(CASE WHEN price = 0 THEN quantity ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
       ) AS [Admissions Free],
    SUM(CASE WHEN price > 0 THEN quantity ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
       ) AS [Admissions Paid],
    SUM(CASE WHEN price > 0 THEN quantity * price ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
        ) AS [Admissions Revenue],
    SUM(quantity)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
        ) AS [Total Admissions]
FROM
    [movies] AS m ;

using window functions:

-- window functions
SELECT 
    -- m.*,
    movie_title, start_date_time,
    price, quantity,

    SUM(CASE WHEN price = 0 THEN quantity ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         RANGE BETWEEN UNBOUNDED PRECEDING
                   AND CURRENT ROW
       ) AS [Admissions Free],
    SUM(CASE WHEN price > 0 THEN quantity ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         RANGE BETWEEN UNBOUNDED PRECEDING
                   AND CURRENT ROW
       ) AS [Admissions Paid],
    SUM(CASE WHEN price > 0 THEN quantity * price ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         RANGE BETWEEN UNBOUNDED PRECEDING
                   AND CURRENT ROW
        ) AS [Admissions Revenue],
    SUM(quantity)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         RANGE BETWEEN UNBOUNDED PRECEDING
                   AND CURRENT ROW
        ) AS [Total Admissions]
FROM
    [movies] AS m ;

*: If there is a UNIQUE constraint on (movie_title, start_date_time), then you could use ROWS instead of RANGE for the window frames (it's usually more efficient). From the comments, there is no such constraint and there could be many rows with same title and datetime, so RANGE is required above.

-- using OUTER APPLY
SELECT 
    -- m.*,
    m.movie_title, m.start_date_time,
    m.price, m.quantity,

    c.[Admissions Free],
    c.[Admissions Paid],
    c.[Admissions Revenue],
    c.[Total Admissions]
FROM
    [movies] AS m
    OUTER APPLY
    ( SELECT
          SUM(CASE WHEN price = 0 THEN quantity ELSE 0 END)
              AS [Admissions Free],
          SUM(CASE WHEN price > 0 THEN quantity ELSE 0 END)
              AS [Admissions Paid],
          SUM(CASE WHEN price > 0 THEN quantity * price ELSE 0 END)
              AS [Admissions Revenue],
          SUM(quantity)
              AS [Total Admissions]
      FROM [movies] AS i
      WHERE i.movie_title = o.movie_title
        AND i.start_date_time <= o.start_date_time
    ) AS c ;

-- using OUTER APPLY
SELECT 
    -- m.*,
    m.movie_title, m.start_date_time,
    m.price, m.quantity,

    c.[Admissions Free],
    c.[Admissions Paid],
    c.[Admissions Revenue],
    c.[Total Admissions]
FROM
    [movies] AS m
    OUTER APPLY
    ( SELECT
          SUM(CASE WHEN i.price = 0 THEN i.quantity ELSE 0 END)
              AS [Admissions Free],
          SUM(CASE WHEN i.price > 0 THEN i.quantity ELSE 0 END)
              AS [Admissions Paid],
          SUM(CASE WHEN i.price > 0 THEN i.quantity * i.price ELSE 0 END)
              AS [Admissions Revenue],
          SUM(i.quantity)
              AS [Total Admissions]
      FROM [movies] AS i
      WHERE i.movie_title = o.movie_title
        AND i.start_date_time <= o.start_date_time
    ) AS c ;

I would try using window functions instead of the four correlated subqueries.

SELECT 
    -- m.*,
    movie_title, start_date_time,
    price, quantity,

    SUM(CASE WHEN price = 0 THEN quantity ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
       ) AS [Admissions Free],
    SUM(CASE WHEN price > 0 THEN quantity ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
       ) AS [Admissions Paid],
    SUM(CASE WHEN price > 0 THEN quantity * price ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
        ) AS [Admissions Revenue],
    SUM(quantity)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
        ) AS [Total Admissions]
FROM
    [movies] AS m ;

I would try using window functions instead of the four correlated subqueries. Or a single correlated subquery (with OUTER APPLY) and see which of the two indexes is used.
Both ideas are to coerce the optimizer to use a single index scan to gather the rolling sums instead of 4 (that both your plans do).

-- window functions
SELECT 
    -- m.*,
    movie_title, start_date_time,
    price, quantity,

    SUM(CASE WHEN price = 0 THEN quantity ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
       ) AS [Admissions Free],
    SUM(CASE WHEN price > 0 THEN quantity ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
       ) AS [Admissions Paid],
    SUM(CASE WHEN price > 0 THEN quantity * price ELSE 0 END)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
        ) AS [Admissions Revenue],
    SUM(quantity)
        OVER
        (PARTITION BY movie_title
         ORDER BY start_date_time
         ROWS BETWEEN UNBOUNDED PRECEDING
                  AND CURRENT ROW
        ) AS [Total Admissions]
FROM
    [movies] AS m ;

using OUTER APPLY:

-- using OUTER APPLY
SELECT 
    -- m.*,
    m.movie_title, m.start_date_time,
    m.price, m.quantity,

    c.[Admissions Free],
    c.[Admissions Paid],
    c.[Admissions Revenue],
    c.[Total Admissions]
FROM
    [movies] AS m
    OUTER APPLY
    ( SELECT
          SUM(CASE WHEN price = 0 THEN quantity ELSE 0 END)
              AS [Admissions Free],
          SUM(CASE WHEN price > 0 THEN quantity ELSE 0 END)
              AS [Admissions Paid],
          SUM(CASE WHEN price > 0 THEN quantity * price ELSE 0 END)
              AS [Admissions Revenue],
          SUM(quantity)
              AS [Total Admissions]
      FROM [movies] AS i
      WHERE i.movie_title = o.movie_title
        AND i.start_date_time <= o.start_date_time
    ) AS c ;