Tell it what you want to stream at and it'll tell you if your computer can handle gaming and streaming at the same time — or whether you need a capture card, a second PC, or an upgrade. Everything runs in your browser; nothing is sent anywhere.
Streaming adds a second full-time job for your computer on top of the game: encoding video in real time and sending it out over your connection. Whether your PC can do both at once without the game stuttering or the stream dropping frames comes down to one core question — is something other than your main CPU doing the encoding, or is the CPU splitting its attention between the game and encoding at the same time?
A modern Nvidia, AMD, or Intel GPU with a dedicated hardware encoder (NVENC, AMF, or Quick Sync) handles the encoding almost entirely on its own silicon, mostly separate from whatever the GPU is doing to render the game — this is why a hardware encoder makes such a large practical difference. Without one, OBS falls back to software encoding (x264), which runs on the same CPU cores that are also running the game, OBS's own overhead, and anything else open in the background. That's the single biggest reason two PCs with similar specs can have very different streaming experiences: one has a free encoder sitting on the GPU, the other is asking the CPU to do everything at once.
Core count matters even with a hardware encoder present, just less dramatically — the CPU still has to run the game, OBS's compositing and scene switching, and background apps like Discord or a browser. A CPU with only 4 cores can bottleneck even a great GPU encoder simply from being asked to juggle too much at once. This is exactly why the check above weighs both your GPU's encoder and your core count rather than just one or the other.