A company that wants to get the best person they can for their job, will ask for and check references. Many other companies know they are supposed to ask for references, but to actually check them is too much trouble, they figure they've already figured out the best person to hire, and they don't bother to check the references. And some companies know they are supposed to ask for references, but don't even intend to use them. If you can provide references, you're probably good.
There are many, many companies that don't check references. But they are taking the chance that they are making an offer to someone who presents well, but has a glaring problem that is easily found, if they only checked a few references. Checking references doesn't ensure you get a good hire, but it does increase the chances.
But that isn't your problem. You had the references available, and got the job. Unfortunately, you also now know that you're working for a company that is relying a bit on chance to get good employees (and which means your new co-workers may or may not be quite as good as you hoped).