The gemara emphasizes that Hashem doesn't need the light of the Menorah because all 40 years that the Jews were in the dessert they were led by the light of Hashem. Therefore the light of the menorah, and particularly the Ner Ma'aravi was an indication that the presence of Hashem is with the Jewish people. The gemara also says that the windows in the Beis HaMikdash were wide on the inside and narrow on the outside to funnel the inner light out to the world, as opposed to enabling sunlight to come from outside.
Tosafos says that a similar gemara in Shabbos makes a point of saying tha Aharon didn't need the light of the Menorah, as opposed to our gemara where the emphasis is on Hashem. I would suggest that they are both true. At the beginning of Parshas B'ha'aloscha the pasuk says אל מול פני המנורה יאירו שבעת הנרות. Rashi explains that the Menorah was designed so that the 6 candles, 3 on each side, faced the center candle "Why? So that people should say that He needs the light". The Maharal explains that normally one designs a candelabra so that each candle shines in a different direction to light up the larger area. The fact that all candles faced the center is symbolic of the fact that Hashem doesn't need the light. The pasuk then continues "ויעש כן אהרן אל מול פני המנורה העלה נרותיה" and Rashi explains that this is too show the praise of Aharon that he didn't deviate in any way from what he was told. The commentaries are very troubled with this pasuk. We are speaking of Aharon the Kohein, the brother of Moshe Rabbeinu - who would think that he would deviate from the way things were done? The Maharal says that he made special effort to be meticulous so that each wick faced the middle candle. This was s delicate detail that one could have been lax in, yet Aharon did it with great precision. To build on this approach, the pasuk is trying to teach that aside from Aharon lighting the candles all facing center to show that Hashem doesn't need the light, he also did this to show that he who will be working in the mishkan, doesn't need the light. When Aharon did the lighting of the menorah to face the middle, he did so with the intention of showing that Hashem doesn't require the light and that he doesn't need the light. This pasuk may be the source of both our gemara which says that the way the menorah was lit shows that Hashem doesn't need the light, and the gemara in Shabbos which says that it shows that Aharon doesn't need the light.