I am in the US. Since PHAnderson isn't selling his easy-to-use display anymore, am I right in thinking it would be smarter for me to buy from an overseas supplier of Axe134Y than try to adapt a product designed for Arduino?
Unfortunately PHAnderson sadly passed away some time ago and the site is mostly a memorial repository for the fine and valuable work he contributed in supporting the PICAXE and other devices.
Our AXE134Y, along with the rest of our 'AXE13x' range, are designed to interface to PICAXE using a single signal wire plus power and can be controlled by simple SEROUT commands. This makes them much easier to use than other displays and modules which aren't specifically designed for PICAXE use, which is why we recommend them.
Direct driving of parallel displays, or those with I2C or SPI interfaces, is possible but is rather more complicated, in terms of connections and control, and figuring out how to control them. It's not impossible but, for 'an easy life', a serial driven display is best.