I've never gamed on a laptop before, but I'm pretty sure anything with a CPU clock speed above 2ghz (3ghz is even better) and a dedicated graphics card of any kind is all you need. As long as you can check those two boxes, it should work. Ideally the laptop would also have an SSD, but that's less to do with FFXI and more to do with general performance.

Unfortunately, anything with dedicated graphics is going to run up the price a fair bit. And some that don't have dedicated graphics show up in Amazon search results even if you say dedicated graphics only, so it can require a bit more browsing through spec sheets than I have the patience for at the moment.

This might be a good starting point: https://www.amazon.com/s?i=computers&bbn=565108&rh=n%3A565108%2Cp_n_graphics_type_browse-bin%3A14292273011%2Cp_computer_cpu_speed-bin%3A2+to+2.9+GHz%7C3+GHz+%26+Up&dc&qid=1623191382&rnid=107455011&ref=sr_nr_p_computer_cpu_speed-bin_3

Avoid Lenovo, they're trash tier and have literally been caught on multiple occasions selling PCs with spyware/adware preinstalled on them. Also, in my personal experience, HP are cheaply built and don't last long.

Looks like most companies have good ones in the $800 price range. There's also this one which looks suspiciously cheap and just barely meets the requirements I set out above. Still, it has dedicated graphics, which likely puts it ahead of the one you were originally scoping out even though the CPU is only about half as fast.

Again though, I've never actually played on a laptop, so take my advice with a grain of salt. I hear lots of other people on here saying CPU speed is most important, that doesn't jive with what I know about this game and what I've heard from friends who play on laptops, but it doesn't mean it's wrong.