There are ground planes in both layers, I do not think there are any problems with the GND.
If your PCB is 2 layer you dont have a GND plane rather GND "areas" as seen on your pictures. GND plane is when you dedicate an "entire layer" to GND. I have the same issues with my 2 layer board, spend lots of thinking how to route for low impedance/inductance. However most likely your board will work but will it be at optimum? you may/may not get funny things happening.
I understand what you mean, but making a 4-layer PCB is very expensive for my products. My main products have a big PCB, 380x130mm, 442x177mm and similar, these are special LED screens with HUB75 led modules. Converting these PCBs to 4 layers would greatly increase the cost of the product. Now all my boards with 2 layers work well with NXP Kinetis MK66, I hope they also work well with RT1020.
I always route manually and very carefully to avoid problems, and now with the RT1020, for the QSPI and the SDRAM, as they handle very fast signals, I will use the meander function of Eagle, to adjust the length of the tracks the same length. I also add vías to join both GND planes, avoiding bare copper areas on any of the faces.
I only had to make some designs to 4 layers, for clients that needed to pass the EMI emission certificate. One of those boards was made in the begining to 2 layers and did not pass the emission tests (picture attached), although almost, and I preferred to redo the board to 4 layers, as it was a small board did not increase the cost too much.
I trust that it can work well with 2-layer plates, in fact I think the NXP evaluation board for the RT1020, is made in 2 layers, or so I thought I read somewhere.