There is no good introductory textbook on dependency grammar (DG) in English that I am aware of; certainly nothing at the level of Linda Thomas' book, which is really very basic. The books linked to in the question are not appropriate: Kahane's book is a collection of essays that are not accessible to aspiring linguists. Liu's book is in Chinese. There are, however, a couple of good introductory texts on DG for those who know German, especially Eroms (2000). But unless stated otherwise, I will assume that you do not read German.
There is another point that is worth noting in this area. When a syntax textbook mentions the word dependency or dependencies, it does not mean that it is a DG. Phrase structure grammars (= constituency grammars) also acknowledge dependencies, especially when they are discussing "long distance dependencies". Dependency grammars tend to use the terms dependency-based or simply dependency grammar in order to distinguish themselves from constituency grammars. Thus many of the books lower down on the page that is linked to in the question are actually constituency grammars, not DGs.
Here's another interesting point that is worth acknowledging when investigating DG. All DGs are hyper-aware of the fact that they are dependency-based, whereas many constituency grammars (which is by far the majority of grammars) are ignorant of dependency-based syntax. With only a couple of exceptions (Matthews 1981, van Valin 2001, Carnie 2010), most syntax textbooks ignore DG (almost) entirely. The situation is now changing, though, especially in computational linguistics.
There are, however, now a couple of accessible encyclopedia articles on DG that have just very recently appeared, both of which I have written:
Routledge Encyclopedia of Syntax
HSK Handbook Syntax -- Theory and Analysis
If you are interested in taking a look at these articles, send me an email (email@example.com); I will hook you up with them.
Finally, if there is a real interest in DG that develops, then time spent with Tesniere's book Elements of Structural Syntax would be a good investment. The history of modern DG begins with Tesniere's monumental work (1959). Tesniere's book remained untranslated into English for decades. But now that situation has just changed (since February 11th), since Sylvain Kahane and I translated the book to English:
I may be able to hook you up with a copy of this tome, too, if you contact me. Note that Tesniere's book begins at a rather basic level, and builds, and builds, and builds, for almost 700 pages.