Would blowing someone else's candle out make mine shine brighter? 
Is the claim in this sign correct? Would a candle shine slightly brighter with slightly more oxygen in the room?
And what do you mean "The candles aren't literal."? 
 A: The claim is certainly true for candles in different rooms. Even in the same room, the effect of one candle on another in terms of oxygen consumption is with all likelihood completely negligible, and the candles could thus be treated as completely separate systems.
As to your question about how the candles are not literal: The sign is a metaphor for how sabotaging someone else does not make you absolutely better, only relatively, which is not the kind that matters (and makes the total situation worse, since you now have less total light / talent / whatever).
Note that if oxygen is a very limited resource, blowing out one candle would make the others burn longer. In much the same way the metaphor does not work in a competition over limited resources. But in the physical situation, infinite oxygen is usually a good approximation.
A: It doesn't burn brighter but rather longer. Given the desity of air in that system remain constant, the amount of oxygen consumed by the candle per unit time is constant and consistent regardless of the number of candles in the system. To put that into perspective, blowing on a flame brightens it because setting air in motion requires compressing it forward layer by layer of molecules, it's this dense cloud of air that provides more oxygen per unit volume to the fuel increasing the combustion rate. So I'll advise not to blow out someone else's candle coz yours won't budge because of that, and you'll never know if you'll live long enough to witness yours burnout.
A: I think it would look as though it would shine more brightly and this is more to do with the eyes response to light stimuli. 
For example, a candle in daylight doesn’t seem  as bright as a candle in the dark.  
A: The quote is TRUE for most candles, in most conditions, for most people. Both the literal and the philosophical can use this quote, as the candle is a candle AND the candle is a metaphor for the light that shines within each of us.
The quote is NOT true for people living in their own darkness of immaturity or an inflated delicate ego.
This person believes
- If there are 2 identical candles in the darkness, they will
appear equally bright.
And
- If this person blows out my candle, only their candle will
be shining in the darkness.
Therefore
- Their candle will shine brighter than mine, as my candle
no longer shines in their darkness.
Sadly this person is trapped in their own darkness, too afraid their light is gone if it’s no longer the brightest light they see.
