Per https://dev.mysql.com/doc/refman/8.0/en/with.html and MySQL "WITH" clause - WITH is only supported on MySQL 8+. Ensure you're using an appropriate version of MySQL
COnverting to a nested version isn't hard. We take your working sql:
with ratings_by_user as (
select occupation, user_id, count(*) num_ratings
from ratings
group by 1,2
),
max_ratings_by_occupation as (
select occupation, max(num_ratings) as max_ratings
from ratings_by_user
group by 1
),
select occupation, user_id
from ratings_by_user
inner join max_ratings_by_occupation
using (occupation)
where num_ratings = max_ratings
we copy everything including the brackets of the WITH, and paste it in before the use of the alias.
step 1, cut the ratings_by_user and paste it in everwhere the ratings_by_user is used (twice)
--cut from here
with ratings_by_user as ,
max_ratings_by_occupation as (
select occupation, max(num_ratings) as max_ratings
from 
  --paste to here
  (
    select occupation, user_id, count(*) num_ratings
    from ratings
    group by 1,2
  ) ratings_by_user
group by 1
),
select occupation, user_id
from
--and also paste to here 
(
  select occupation, user_id, count(*) num_ratings
  from ratings
  group by 1,2
) ratings_by_user
inner join max_ratings_by_occupation
using (occupation)
where num_ratings = max_ratings
step 2, cut the max_ratings_by_occupation in and paste it in where it's used:
with ratings_by_user as ,
--cut from here
max_ratings_by_occupation as ,
select occupation, user_id
from
(
  select occupation, user_id, count(*) num_ratings
  from ratings
  group by 1,2
) ratings_by_user
inner join 
--paste to here
(
  select occupation, max(num_ratings) as max_ratings
  from 
  (
    select occupation, user_id, count(*) num_ratings
    from ratings
    group by 1,2
  ) ratings_by_user
  group by 1
) max_ratings_by_occupation
using (occupation)
where num_ratings = max_ratings
step 3, clean up the empty withs
select occupation, user_id
from
(
  select occupation, user_id, count(*) num_ratings
  from ratings
  group by 1,2
) ratings_by_user
inner join 
(
  select occupation, max(num_ratings) as max_ratings
  from 
  (
    select occupation, user_id, count(*) num_ratings
    from ratings
    group by 1,2
  ) ratings_by_user
  group by 1
) max_ratings_by_occupation
using (occupation)
where num_ratings = max_ratings
This would be a start for optimizing/rewriting. The tricky part for this was that it uses ratings_by_user twice, so two pastes were needed in step 1
Your reformat attempt didn't work out because you were trying to use, at an outer level, a resultset that only existed at an inner level:
select occupation, user_id, count(*) as num_ratings
from 
( --max_ratings_table available inside these brackets
    select occupation, max(num_ratings) max_ratings 
    from ( 
        select occupation, user_id, count(*) num_ratings
        from users
        group by 1,2
        ) as ratings_table
    group by 1
    ) as max_ratings_table
  --end of max_ratings_table availability
) 
inner join ratings on ratings.occupation = max_ratings_table.occupation
--                                         ^^^^^^^^^^^^^^^^^
--                                       mrt not available here
where max_ratings = num_ratings