That plug-in looks to be for a specific kind of neural network. You provide inputs and use some training data with the output to tune the weights with the back propagation action. 
For what you want the “deep” basically means taking the pixels of the game screen and using that as an input. Likely applying some convolution to reduce the amount of data first. You may be better off just feeding the NN with inputs directly to simplify things. Probably the x positions of the next three obstacles or something. The output would be whether to jump or not. 
For the “reenforcement learning” that would basically mean running the game multiple times with random weights, then taking the ones that performed the best and run copies of that with slight differences with the weights and repeat. Over time it would converge on a better solution. 
Anyways that’s what I gather from reading on it. Looks to be a vast subject and there is a lot of ideas you can implement. 
Anyways, as a simple example, you could have the x of the two next platforms be the input, and have a hidden layer of two nodes, and an output of one node of whether to jump or not.
Math wise you can calculate whether to jump with the NN like so. 
In0 = tree.x
In1 = tree.x
Hidden0 = 1/(1+exp(-(in0*w0+in1*w1+w2)))
Hidden1 = 1/(1+exp(-(in0*w3+in1*w4+w5)))
Jump = 1/(1+exp(-(hidden0*w6+hidden1*w7+w8)))
You’d need to do some picking so the inputs would be the next two trees. Or if there isn’t any you could set the values to infinity or something. 
The w0 through w8 values is an array of 9 values that make up the brains of your NN. the values apparently are usually in the 0 to 1 range. Initially you’d just use random values and you’d choose one of them to tweak to do a mutation. 
By having the 9 weights in one array it’s easy to duplicate it to make variations. You could even store the distance as instance variables. 
Game loop would be to take one of the arrays, duplicate it and tweak some values of the duplicates. Then run the game with each of them until the player dies and log the distance. Once they are all done keep the best, remove the others and repeat. 
There are likely other improvements but that’s the limit of my knowledge at the moment. It’s likely easier to do better or more advanced things by understanding neural networks better. 
This guy has good videos explaining stuff like that. But you may want written docs at some point. 
m.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw