The optimization process and recommendations:

1. Avoid Subqueries In From Clause (modified query below): The database cannot properly optimize subqueries in the FROM clause. Therefore, we recommend to extract the subqueries to temporary tables, index them and join to them in the outer query.
2. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
3. Push Filtering Conditions Into Subqueries (modified query below): Parts of the WHERE clause can pushed from the outer query to a subquery / union clause. Applying those conditions as early as possible will allow the database to scan less data and run the query more efficiently.

Optimal indexes for this query:

ALTER TABLE `es_temp1` ADD INDEX `es_temp1_idx_name_bib_timed_categ_total_categ` (`Name`,`BIB`,`TimeDerived`,`CategoryName`,`TotalPace`,`Category`);
ALTER TABLE `es_temp2` ADD INDEX `es_temp2_idx_category` (`Category`);

The optimized query:

SELECT
        UCASE(g1.Name) Name,
        g1.BIB,
        g1.TimeDerived,
        g1.CategoryName,
        g1.TotalPace,
        g1.Category,
        COUNT(*) AS rank 
    FROM
        es_temp1 g1 
    JOIN
        es_temp2 g2 
            ON (
                g2.TimeDerived,
            g2.bib) <= (g1.TimeDerived,
            g1.bib) 
            AND g1.Category = g2.Category 
        WHERE
            1 = 1 
            AND 1 = 1 
        GROUP BY
            g1.Name,
            g1.BIB,
            g1.TimeDerived,
            g1.CategoryName,
            g1.TotalPace,
            g1.Category 
        ORDER BY
            g1.Category,
            rank