Beach chair drink pocket, stake or table?
Compare the attachment and resting surface.

Built-in pockets
Check container depth, handle clearance and how the chair fabric moves when occupied. A pocket serves a different role from a tabletop base.
Stakes and clamps
These need suitable ground or chair structure plus permission. Check the exact accessory instructions.
Steadi at a table
Use the full 5.2-inch footprint on a suitable table. The holder travels with a compatible drink without attaching to the chair.