Long story short, the address you give the RAM is a combination of row and column.
The address you provide to the RAM is a certain number of bits depending on the size of the RAM. For a 2K RAM, it's 11 bits. For a 256 byte RAM, it's 8 bits. These bits are divided up to make the row and column addresses. For simplicity's sake, we'll look at a 256 byte RAM. It has 8 address bits, which are divided into 2 4-bit addresses, one for row and one for column. There would be 16 rows x 16 columns, so the upper 4 bits would address the row and the lower 4 bits the column (or vice versa).
Larger RAMs may even go beyond rows and columns, into banks. So, instead of a single matrix, there would be 2 or more. For example, a 64K RAM may be made of 4 16K banks that have 128 rows and 128 columns each. 7 bits of the address would be the row address, 7 bits the column, and 2 bits to select the bank for a total of 16 address bits.
The arrays don't have to be square either. A 32K chip could use a 256 row x 128 column array, for example. In this case there would be a different number of bits in the column and row addresses.
So, in short, physically the RAM is made up of rows, columns and banks, but from an end-user perspective this doesn't matter. You can look at a 256 byte RAM as being a 256x1 array, a 128x2, etc. It all depends on how you interpret the address bits.
Then to add another wrinkle, any RAM that carries more than 1 bit (such as your 2Kx8) actually has a bank of RAM for each bit. They're addressed in parallel to give you the 8 bits. So, if you were to examine your chip under a microscope, you may see 8 separate arrays, or 8 groups of arrays. Many computers use 1-bit RAM, so to get bytes you needed to install 8 chips (back in the day of using DIP package RAM). The DIMMs you see in modern computers has a chip for each bit, which is why there's usually 8 or 16 chips on a DIMM.