NVIDIA K-80 GPU does not run with Deep Learning Image Tensorflow
The problem was with my use of requirements.txt.
I created it on my laptop with pip freeze, uploaded it to the VM and used pip to install all the requirements.
In this way my requirements.txt included tensorflow.  As the result, pip installed the repository version that did not include GPU support, replacing pre-installed tensorflow with GPU support.
I was able to figure this out by repeating my steps and checking GPU per second suggestion of @Shintlor (thanks!) along the way.
I have created another VM and did not use requirements.txt; rather, I installed all the missing packages one by one.  After that my model trains now 20 times faster than on my laptop.
I have created a virtual machine in Google Compute us-east-1c region with the following specifications: n1-standard-2 (2 vCPU, 7.5 GB memory), 1 NVIDIA Tesla K80 GPU, boot disk: Deep Learning Image Tensorflow 1.10.1 m7 CUDA 9.2.
When I first logged in to the machine, it asked me to install the drivers and I agreed.  It gave me some warning messages which I did not save.
I tried to train a model written entirely in Keras with TF backend.
However, judging by the speed and CPU utilization (both similar to what it does on my laptop, slow and using almost all CPU available), GPU is not used.
This is also confirmed by the TF output:

2018-09-21 08:39:48.602158: I
  tensorflow/core/platform/cpu_feature_guard.cc:141] Your CPU supports
  instructions that this TensorFlow binary was not compiled to use: AVX2
  FMA

It did not mention any GPU.  (Thanks @Matias Valdenegro !)
In my model I did not relate to GPU with an understanding that TF takes care of it automatically.
Any ideas?
Many thanks.