What are these cracks in the side of my bicycle tyre called? Does this mean that my tyre is gone?

I'd say, it's time to replace the tire. It doesn't really matter what caused it - could have been low quality, age, or extended use. The cracks mean the layers the tire is made of are separating and in the long run you will see more punctures because the material is softening. A brand-name tire costs 15 to 25 EUR/USD/GBP which I consider low enough to not take the risk of punctures.

For the record, that is called "Dry Rot", and it's caused by rubber drying out and getting less pliable. Commonly happens when a bike is on a concrete floor not being used(like in a garage or storage shed) for a long period of time. It will make your tire brittle, and sometimes will make it unsafe. A little dry rot usually isn't detrimental, a lot can split the sidewall of the tire causing a blowout. Yes, you should change the tire.