First of all, by the 17th-18th centuries, no one was speaking Old English. Old English was long dead by that point. You're talking about a time around the end of the Middle English period and the beginning of Modern English.
Second, as others have mentioned, that German sounding language is in fact Afrikaans, which is very closely related to Dutch (some say they are mutually intelligible, but since this is an English language site, I'll leave it at that).
The British came to South Africa since 17-18th centuries, & settled there. These people somehow still keep their old English language. Just like people living in some area in UK that speak their English dialect that is so different that we can't understand.
What you're missing is that the Dutch colonized South Africa long before the British, which is how Afrikaans came to be spoken there.
They're not speaking Old English, which, by the way, hasn't been spoken since the 12th century, long before the 17th century. Have a look at the Wikipedia entry; you won't recognize any of the words.
Also, when people speak in dialects that are difficult to understand, they still read and write the same way as everyone else. As you'll see, that's not at all possible with Old English.