There is No need to create a new language. Use as example c. Get a chunk of memory with malloc() and do wharever you wish with it.
On a typical operating system today you might need to use low level OS functions of you want to keep the memory from beeing swapped due to virtual memory.
There are two different address spaces, let's call them logical and physical. The addresses a programmer thinks about are the logical addresses, the page table translates logical addresses to physical addresses.
As you point out, paging allows you to sparsely map the logical address space to the physical address space.
But the bold sentences in your quote ...