That document was written as a generic snippet usage explanation before DropMenu was made the default (it was actually written with ListMenuX in mind, but the principles are the same for all snippets. Read the comments at the beginning of your snippet’s code for optional arguments). In DropMenu, if selfAsLink is set to true as an option, a link is generated but the "here" classname is not added to the <li> tag. And DropMenu never adds class names to the <a> elements, only to the <li> and <ul> elements. It leads to cleaner generated HTML code, but often requires trickier CSS code. Here is the DropMenu specific documentation:
http://modxcms.com/snippet-dropmenu.html
(sorry about the lower case l, my poor laptop needs a tuneup for a number of sticky keys, including the left shift key!)
To use ListMenuX, get the code (I attached it here), create a new snippet and copy/paste the code. Then where you have [!DropMenu...!] put [!ListMenuX...!] instead. Read the comments and the settings at the beginning of the snippet’s code to see the optional arguments you can use. For the template you are using in this case, since you need to style both the <li> and the <a> elements for the "sliding doors" technique, you’ll need to set three arguments:
[!ListMenuX?id=`0`&activeLinkClass=`active`&activeListClass=`here`!]
Now you’ll have a menu starting at level 0, 1 level deep (ListMenuX sets the depth to 1 by default), with the active link classes <li class="here"> and <a class="active"> and you can style them both as you like.