Choux pastry (Chocolate eclairs) doesn't rise
It's actually been a few years since I made éclairs, so I might be forgetting a few things, but here are my immediate reactions to the recipe:


"Plain flour" (by which I assume they mean all-purpose flour) is not appropriate for choux paste.  You should be using bread flour (AKA "strong flour"), you need the extra gluten for this.  That is probably the most important reason why your choux paste didn't turn out right.
The ratio of fat to water is off.  You want a 2:1 water:fat ratio.  Use 50 g of butter or shortening for every 100 mL of water.  For reference, if you're going to adjust the ratio then you also want to use approximately 2.4 eggs per 100 mL of water.  The recipe mentioned in the question is close, but slightly short, so be careful if scaling up.
The ratio of flour to water is blatantly wrong, for both the posted recipe and what you say is the cookbook recipe, and you should never ever use volumetric measurements for flour in such a sensitive baking recipe.  You want to measure out 75 g of flour per 100 mL of water.  For a cup of water that's about 175 g of bread flour.  Don't even try to calculate the volume, weigh it.  This is extremely important, if you don't use enough flour then the choux paste won't fully gelatinize!
A "pinch" of salt is probably OK at this small scale, but if you ever decide to scale up then you need to be accurate; use 2% salt (2 g per 100 mL of water).
The recipe is correct in warning you against letting any of the water evaporate, and telling you to cook and stir the roux until it clears the side and forms balls when shaken.  You should also see a white film on the bottom of the pan.
One thing that the recipe doesn't mention that is extremely important is that you need to wait for the roux to cool before adding the eggs.  Whole egg coagulates at 65° C (149° F) so it is absolutely imperative that the roux is cooler than that, otherwise you will end up with scrambled eggs.
Make sure you completely incorporate the eggs.  Scrape the sides of the bowl if necessary.  And don't try to cut corners by adding all the eggs at once; you really need to add them one at a time, otherwise you'll end up with lumps.  Missing this probably won't cause failure to rise, but you don't want lumps, trust me.
When you're done, you should have a paste that resembles the consistency of a meringue, but heavier.  That is, it holds its shape, even against gravity, but is still soft enough to spread.  I check with my finger.  If it's too stiff, you can add milk to soften it, but if it's not stiff enough, then you didn't get enough of the flour gelatinized and your paste is ruined.  (So don't overmilk!)
I don't agree with their "very hot oven, then lower the temperature to 180° C" instruction.  180° C is a very low temperature for baking choux paste, and I don't think that the 10 minutes of "very hot" temperature (whatever that is) are going to compensate for it.  I have always baked choux paste shells at a straight 200° C (390° F) for 30 minutes.


That's about it for tearing apart their choux paste recipe.  I'm not even going to touch their "custard cream" recipe, which is just not even remotely close to the chantilly cream that éclairs are supposed to have.