Red and blue do in fact make purple, but that would be a disgusting look just based on color theory alone. Two vibrant primary colors with a dark secondary color in the middle will make the logo look like it came out of Chuck E Cheese. If there is a change I agree with (although the logo is fine to me), it would be the half blue/half red G.
If that was the thought that was put into the colour choice, they should have used the correct blue colour for the gmod colourcode. A lot of things are ment to take into consideration when a designing a logo tho, and while SGM's current logo may not fulfill the requirements a designer would request, it does fulfill some of the base lines. If a change was required, I would personally make it so that the circle or SGM is given a 90* rotation. So that S would be in 1 half of the circle and the GM in the other half of the Circle, and to create balance in the Logo, make the S larger as well since its clear that the GM belongs together.
Why? Blue and Red are a classic color combination. And I didn't say it was the thought they had behind it, but it's not a wild assumption. The S is for the name of the servers, and the GM is for the game those servers are on. Including purple adds a completely different color into the mix, which I don't think is necessary, other than for the people with OCD.
SGM (Not too bad, also | Owner | Lead | Admin |) SGM (Not a fan, but wanted to see) SGM (This one is actually fitting cause of | Traitor | Innocent | Detective |)
Cause thats how Design works. If you use a colour with the intention to refference (in this case gmod) you would also use a colour refference and use a colour that matches the blue colour of gmod as much as possible. Im well aware what the letters stand for boyo, just saying that refference coulour is important when it comes to design as well as how aesthetic it is. On a side note tho, its not even something that is that important. Just thought it would be fun to talk design and ideas in here, cause creativity is what my education and work is all about ^~^