How do Standing Waves satisfy the criteria in order to be considered as Waves? Why are standing waves even categorised as waves if they don't transfer energy from one point to another?
Waves are generally defined as disturbances that transfer energy but standing waves don't fulfil that criterion. Even though they are formed by the superposition of two travelling waves (of the same frequency) but if we just consider the resultant standing wave, I am not sure that how a standing wave can be considered as a wave in the first place.
 A: Energy is being transported. A standing wave can be written as a superposition of a left-moving wave, which transports energy to the left, and a right-moving wave, which transports energy to the right. For a standing wave, it happens that there is no net transfer of energy to the right or to the left. But there are still processes transferring energy around the string. A standing wave is clearly different from a string at rest.
Let's try an economic analogy, although as a warning analogies are prone to breaking down. My analogy is that we could say that an economy is the transfer of goods and services. If the exports and imports into a country balance out, there is still trade occurring and therefore an active economy, even though the net trade is zero. The economy is different from the state where no trade of any kind is occuring.
A: Wave is a rather generic and imprecise term, encompassing many situations which are hard to unify - see, e.g., the discussions here and here. There are many reasons to count standing waves among waves, the most looming among which are:

*

*they are periodic in space in time, which is a common feature of waves (although this is not the case of shock waves and solitons)

*they are solutions of wave equations.

A: Standing waves should not be considered waves, but rather excitations of an oscillator. Nothing "real" can be thought not to expand both in space and time. But when observing something "real" the spacial or timely behaviour of the "real" can be dominant. Also we consider waves to be something that is periodical. This period can be in time, in space or in time and space. The first we call "oscillation", the second sometimes lattice, sometimes wavy and the third "a wave".
Standing waves do not show a changing spacial phase but only changing amplitude. So they should be seen as an oscillation which is implemented in limited space.
This may be best illustrated by a laser where mirrors define a spacial area, the surface of the mirror determines the short circuit to reflect the EM-radiation and as one of the mirrors leaks a fraction of the energy stored in the cavity we inside see oscillation and outside a wave.
