Sounds like 2 separate problems.
The boss doesn't understand the purpose of email or the concept of User Experience. See other questions and answers for that, e.g. How do you persuade an organization to value UX
Responsive datatables. There are two main options: the layout as you describe, and the card UI design as Juan has pointed out. (Scrolling using overflow doesn't work on many email clients, and automatically hiding columns relies on JavaScript, which obviously doesn't work.)
Traditional datatable: no
Emails on mobile can comfortably display up to about 5-6 thin columns, so your layout is never going to be responsive unless you hide most of the columns on the email, and allow them to click through for more information (on a website, where you can use JavaScript solutions).
Card UI Design
Essentially, this pulls the data out of a table completely, opting for a 'card' which enables you to use multiple rows for a single entry. Then, you complement this with graphical hierarchy to create a pleasing display that responds to screen width naturally. There are tricks to make it more accessible and durable too, as I describe in my post: Responsive DataTables through Card UI Design for Email
You may end up with something like this, which just uses simple tables (no media queries, no hiding, fully and totally compatible with every email client). It reduced 6 columns to 3, and grouped together the data which goes together, making it much easier to read:
Before:

Card UI Design makeover:
