The reason is that LinearSolve by default parallelizes computations while other functions involved can use only one thread. So when you run almost pure LinearSolve code it uses 4 threads and you get 50% processor load by MathKernel (because you have 8 virtual cores due to hyperthreading). When you run your "graphical" code MathKernel uses only one core and the actual processor load is 1/8 = 0.125. You can get significant speedup simply by replacing Table with ParallelTable:

Graphics[{Thickness[0.001], 
       ParallelTable[{Hue[Random[]], Line /@ 
             Nest[Flatten[RandomSpike /@ #1, 1] & , 
               startTriangle, 4]}, {48}]}] // Timing