First of all, if you default on the InnoDB storage engine of MySQL, then there is no way you can update data without row locks except setting the transaction isolation level down to READ UNCOMMITTED by running
SET TRANSACTION ISOLATION LEVEL READ UNCOMMITTED;
However, I don't think the database behavior is what you expect since the dirty read is allowed in this case. READ UNCOMMITTED is rarely useful in practice.
To complement the answer from @Tim, it is indeed a good idea to have a unique index on the column used in the where clause. However, please note as well that there is no absolute guarantee that the optimizer will eventually choose such execution plan using the index created. It may work or not work, depending on the case.
For your case, what you could do is to split the long transaction into multiple short transactions. Instead of updating millions of rows in one shot, scanning only thousands of rows each time would be better. The X locks are released when each short transaction commits or rollbacks, giving the concurrent updates the opportunity to go ahead.
By the way, I assume that your batch has lower priority than the other online processes, thus it could be scheduled out of peak hours to further minimize the impact.
P.S. The IX lock is not on the record itself, but attached to the higher-granularity table object. And even with REPEATABLE READ transaction isolation level, there is no gap lock when the query uses a unique index.