iRule for redirection with masking for a specific URI only.

Have a look at this answer:

https://devcentral.f5.com/questions/uri-translation-vs-httpredirect-irule-52327

I modified your iRule, you will have to test:

when HTTP_REQUEST {
    if { [HTTP::uri] starts_with "/manual/" } {
        HTTP::header replace "Host" "www.newsite.com"
        set uri [string range [HTTP::uri] 8 end]
        HTTP::uri "/support/txt/docs/$uri" 
    }
}

The logic is correct, but you had multiple syntax errors. Also, you need to send the remaining of the URI to the server.