The first sentence is a compound sentence and 'WE' is the subject of coordinate clause beginning with "simulate the way, and, of course, there is a subordinate clause beginning with(as/by which/in the like manner)a human user... data. It means:
Our approach is to show you the page content and how to navigate it as like a human user.
Before we embark on analysing the second option, the '—+ing' form used here is a participle. Simply put "+ing" form of verb discharge four functions depending on usage.
• to make tense
• to work as noun
• to work as adjective
• to work as pure noun(the +—ing + of)
In our example it is a present participle (adjective). Such +—ing formed participles have no subject. It mostly has its subject in the preceding clause to which it refers.
•The boy(who is) standing at the gate, is my brother.
But such construction often takes us unawares. As —
•I saw a dead cow walking along the street.
We know how to rearrange the sentence meaningfully. Begin the sentence with ' walking along the stree,'.
In the second sentence simulating refers to ' page content', and, thus, drastically changing the meaning. I think we have somehow make you understand the use of participle phrase. Would It not be better to place "simulating... data" after " in our approach"? In that case both the sentences mean exactly the same.