This is interesting, my DS is also in Y2, currently enjoys Beast Quest and Jack Stalwart books, and is bilingual with both parents being non-native English speakers (though I am pretty close, as I grew up bilingually myself with English as the minority language).
So far I figured he will pick up the vocabulary 'automatically' given that he reads a lot. No, he won't understand every new word he encounters, but will make an interpretation from context, and after having encountered it a few times, will have a good idea of what it means. If I remember correctly, that is pretty much how I learned most of my vocabulary, in both my languages.
I figured I'd leave 'direct instruction' to school.
Also I found that recently, DS quite often asks what a word means in conversation. And even when I 'know' exactly what the word is, and can give him the translation, that is, the same word in our other language, I still often can't explain it very well to him. I used that word because that is the word that fits the situation, and it is not the same as any other word I could have used; perhaps 'a bit like ...' but still different. The nuances of word meanings and word usages IMO can't really be explained but must be 'experienced'.
After reflection triggered by this thread though I think we'll get one of those electronic dictionary bookmark thingies, and see how he gets on with it. The thought process being: Yes he will pick up a lot of vocab from reading and will work out what the words mean, but to compare with other children, they will do this too but will ALSO reinforce that understanding of words in their conversations with their parents. Whereas we do our very best to speak to the kids in our home language as much as possible, as they won't pick that up casually anywhere else.
So we'll give the dictionary a go, but if it turns out to be to the detriment of his enjoyment of reading, we won't push it.
P.S.
Seeing as your DS seems to be into similar books, anything else you can recommend?
Our DS seems to also like Flying Fergus, Astrosaurs, The Secret Rescuers; today he devoured his first 'Time Hunters' book; he's keen on the idea of Fizzlebert Stump but hasn't started yet. Really enjoyed The Enchanted Wood series (Enid Blyton) and some Roald Dahl but those he very much wanted to share, so they mostly ended up being on the 'us reading to him' pile.