It was more gamey, you always first had the cave river, then the cavern, then the magma sea, then the glowing pits, then the candy, and when you dug candy it started checking for you randomly lose the game. Each step had enemies increasing in strength. It also had the different guild masters come in. You didn't have the manager screen until a manager showed up. You'd get your first anvil with a metalsmith at the end of the first year. You couldn't build walls and other constructions. There were cave-ins if you dug 7x7 or larger areas. You could flood the world permanently. Ummm, that's about all I can remember.
There weren't random types of ores - all the ores you got were segregated by "layer" you were digging through in the game. Copper was lower-class and closer to the surface. Iron was more valuable, so you only got to find it deeper down, past the first few obstacles.
In 2d, those cave rivers, chasms, and magma rivers were all completely unbypassable. They were roadblocks and challenges you had to tackle, and existed as one of the primary means of generating that "gamey" escalating difficulty as you progress through the game. They extend infinitely in the Y-axis, so the only way to get past each "roadblock" was to build a bridge over them. Cave rivers flooded, and would occasionally sweep people crossing this bridge away. Each type of river or chasm would also spawn enemies, and there was no way to wall these off - you just had to station soldiers in your prime hallways at all times.
Each successive type of river or chasm would spawn harder and harder enemies. Meanwhile, clearing each successive river or chasm would give you access to better resources. For example, you had to clear the chasm to get to iron. You had to get up to the magma river to start up those easy-peasy magma forges. But then, magma rivers spawn fire imps that you can't block off so easily, and will set your dwarves on fire, which is always fatal and potentially fortress-ending if you are not careful. You also get gremlins from chasms, which can wreak havoc by pulling levers, and can bypass all your normal security measures while staying invisible - these add a "fun" layer of difficulty, because not every threat to your fortress is just a monster who fights normally.
Farms also had to be flooded via the cave river once a year or would not function. This meant, in practical terms, farms had to be built near the cave river, and use a pump to flood the fields early in the year. This, in turn, meant that farms weren't quite so brain-dead a thing to set up.
Basically, when people say 2d was more "gamey", they mean it had an escalating series of challenges for you as a player, and each successive roadblock you clear was a clearly distinguished clear step up in challenge, but also rewards and prestige as a player.
This is as opposed to the current game, where all the challenge is pretty much up-front (except for maybe a particularly nasty FB or releasing the HFS), where the game is "hard" for new people simply because they haven't learned, but once you clear your first game year, you will find the game very easy and repetitive because the only challenge is in making a self-sustaining fort that funnels all external threats into a single killzone kept apart from the civilian populace. Things like vampires help, but basically, part of why I've been arguing for advanced farming, rubble/cave-ins/gas explosions in mining, and now the increasing levels of challenge in the Class Warfare thread is that the game needs to recapture the notion that it should be easier early on, and gain successively more complex challenges as you go forward.