The candle burns (approximately) all of the oxygen, reducing the volume of gas inside the cup by 20%, which causes the water level inside the cup to rise in order to equalize the pressure of the gas inside the glass with that of the atmosphere.
If the interpretation is right, where does the oxygen go?
In truth, the oxygen is replaced by CO2. Pretty much every oxygen molecule that's burned (i.e. combined with carbon) becomes one molecule of CO2. Therefore the amount of gas should remain unchanged.
There is another effect at work. When you put the bowl over the top the air is warm, and being warmed, but the flame. Some of the air trapped is pushed out - if you do this you can see bubbles around the rim - and then the remaining air cools. It's that cooling that sucks in the water.
The demonstration is, indeed, really poor.