FFXIV is an MMORPG. Similar to WoW it is an MMO, but before that, it is an RPG, and still even before that it is Final Fantasy.
If you don't want to p2p then you can play those f2p/p2w games with cash shops. Depending on your play style you might even end up paying more compared to a subscription fee mmorpg.
In FFXIV a patch like 2.2 "Through the Maelstrom" is like a full expansion pack compared to those other games you can play for free. You're guaranteed constant updates and added content every 2-3 months. This is what people pay for.