I agree that the rise of MySQL is combined with using RDBMS as a table store rather than a relational database, but I am not positive that this was driven by RoR and ORMs. Every large-scale system I have worked with that utilizes MySQL (and I'm on at least my third in a row of these systems, sadly!) is/was driven by application-logic database utilization via the "FriendFeed model" - that is, a big fat ID->Document Blob table for persistence and breakout tables for indexing.

ORMs and ActiveRecord in particular encourage, to some extent, the use of a RDBMS, even if they didn't get to take advantage of them well for a long time - for example, in RoR "has_one / has_many" for foreign-key relationship, .joins(:field_name) for, well, joins, and so on.