Query A is the same as:
select 'true' where 3 = 1 or 3 = 2 or 3 = 3 or 3 = null
Since 3 = 3 is true, you get a result.
Query B is the same as:
select 'true' where 3 <> 1 and 3 <> 2 and 3 <> null
When ansi_nulls is on, 3 <> null is UNKNOWN, so the predicate evaluates to UNKNOWN, and you don’t get any rows.
When ansi_nulls is off, 3 <> null is true, so the predicate evaluates to true, and you get a row.