question about cores

Again... "it's complicated" and "it depends".

If you want a bit of an explanation I'll have a go... but without specific CPUs and specific workloads (i.e. specific games), we can only really speculate.

At a very basic level there are 3 key factors which influence CPU performance:
1) Instructions Per Cycle (IPC): This is essentially how much work each CPU core can complete per clock cycle
2) Frequency: the number of clock cycles per second (measured in Ghz)
3) Number of cores

Frequency and Cores are listed on every CPU product, while IPC is much harder to quantify because it depends entirely on the workload. AMD CPUs at the moment can offer very high frequencies and lots of cores, but for most tasks their IPC is so poor that competing Intel CPUs usually get more work done despite having lower frequencies and fewer cores.

Having more cores sounds great, a quad core CPU should be theoretically twice as fast as a dual core at the same frequency and IPC. The problem is that you need a workload that can be divided into four parts which are not reliant on each other in any way. It's actually not dissimilar to a human workplace. There are some jobs where simply having more staff (like adding more cores) will improve output. For other jobs/tasks however, there will be certain roles or sub-tasks which impact all the others, so having extra staff (like extra cores) will simply result in some people waiting around for chunks of time while the one or two people key people finish those key tasks.

Workloads like video encoding scale really well with extra cores. Because there is an entire video to be rendered, it can simply be chunked into as many pieces as required and each core can operate independently on its own section without impacting or having to wait on the others. In cases like these you can see almost perfect scaling, where a quad core will be pretty much twice as fast as a dual core assuming the same IPC and frequency.

It's much more difficult, on the other hand, to effectively utilise extra cores in most video games. CPUs in video games handle things like collision detection, physics, AI, and the prep work required by the graphics card. But those things are not independent of one another. How can an AI algorithm running on one core know what to do until the collision detection process runs and tells it whether it's been hit by a bullet or not? You can't start submitting draw calls to a video card until you know whether a rocket has exploded or not, etc, etc.

So that's why traditionally games have preferred a few fast cores over a greater number of slower cores. We are starting to see games that scale well with four cores, and core hungry games will grow more common as games get more complicated and developers learn ways of better utilising CPU resources. BUT, even games that scale well with four cores rarely (I'd say never at this stage) actually tax all of those cores equally. What you'll see is one or two cores being slammed 100% and then the remaining cores with some work to do, but they're not being pushed near as hard. That's why dual cores, and particularly i3s with hyperthreading tend to hold up pretty well, even in games that make use of quad cores.

In terms of "quad core as a minimum requirement"... depends entirely on the game. Minimum requirements are often entirely contradictory and nonsense. As I said above, the i3s often hold up really well and in some cases are significantly faster than a (sort of) 8 core AMD processor at 5Ghz. But no doubt there are a few games out there that close to 100% tax two cores, and then still have sufficient work for extra cores such than an i3 becomes a problem... and a Pentium (dual core no hyperthreading) becomes pretty unplayable. At the moment though, those games are pretty rare IMHO.