Mysql – dynamic or static database tables

Your issues are probably less about performance, assuming reasonable equipment and a good indexing structure, and more about other impacts that you face.

Approach 1 means some additional programming complexity to deal with filtering rows in each table to restrict access to a single gameworld. It also means that if you need to restore a gameworld, you would have to (a) restore all gameworlds (since they are in the same database) or (b) restore the one database to a recovery database and then script the appropriate gameworld data from Recovery to your Gameworlds database.

Approach 2 means that you need to be able to manage schema changes across many databases. This can be done by scripting as needed. It is also easier to choose to have different schemas for some gameworlds, but that adds management overhead. However, if a a single gameworld crashes, you can restore the latest good backup(s) and get it going again.

Some years ago some Microsoft folks wrote up their take on Multi-Tenanted databases. See: http://msdn.microsoft.com/en-us/library/aa479086.aspx

Having more tables should not, in itself, cause performance problems within the size range you describe.

Choosing your approach should take into account leveraging your strengths so that you have a system you (and your project members) can readily manage.

If a session can only belong to a single user at any given time, the more appropriate model would be without a join table (user_sessions). What's the problem with column user_id being NULL?

If you need it to be NOT NULL and you don't always know the user at creation time, just insert a user "unknown" (with user_id 0 in my example). Can serve as DEFAULT value, too ...

CREATE TABLE sessions
  session_id   serial PRIMARY KEY
 ,user_id      int NOT NULL DEFAULT 0 REFERENCES users(user_id)
 ,session_date timestamp
 ...
)

Note on indexing strategy

Postgres can combine multiple indices with excellent speed. Typically, in your original scenario, with a nested loop:

nested loop join: The right relation is scanned once for every row found in the left relation. This strategy is easy to implement but can be very time consuming. (However, if the right relation can be scanned with an index scan, this can be a good strategy. It is possible to use values from the current row of the left relation as keys for the index scan of the right.)

Say, you have these indices:

sesssions(session_id)
user_sessions(session_id, user_id)

Both should be covered by the pk constraints in your original model automatically. However, the second one could go either way (user_id, session_id) or (session_id, user_id) and that matters:
Is a composite index also good for queries on the first field?

For best performance in a query like:

SELECT u.user_name, s.session_date 
FROM   users         u
JOIN   user_sessions us USING (user_id)
JOIN   sessions      s  USING (session_id)
WHERE  u.user_name = 'foo'

You would need the index (or pk constraint) to be

user_sessions(user_id, session_id)

Or have an additional index with user_id as first column.