Reuse previous value in window function
This likely needs a recursive CTE, since you want the value of the column to depend on the value of the previous (calculated) value of the same column.
(Recursive CTEs are available in MariaDB since version 10.2.2)

I assume that (date) is unique, otherwise the result will be non-deterministic:

WITH RECURSIVE
  t AS
  ( 
    SELECT
        date, col2,
        ROW_NUMBER() OVER (ORDER BY date) AS rn
    FROM 
        tableX
  ), 
  cte AS 
  ( 
    SELECT 
        date, col2, rn,
        CAST(1 AS DECIMAL(10,3)) AS col1     -- starting value
    FROM 
        t
    WHERE
        rn = 1

    UNION ALL

    SELECT 
        t.date, t.col2, t.rn,
        (c.col1 + 1) * t.col2                -- calculate col1
    FROM 
        t JOIN cte AS c
        ON t.rn = c.rn + 1
   )
SELECT date, col2, col1
FROM cte ;


Tested at: dbfiddle.uk