I'm seeing the same thing - was working in Yosemite, did not work in Sierra with no other changes. Interestingly "netstat" and "route" disagree on the gateway for the DNS server:
default 192.168.1.254 UGSc 12 0 en1
10 172.16.0.57 UGSc 0 0 utun1
127 127.0.0.1 UCS 0 0 lo0
127.0.0.1 127.0.0.1 UH 3 5138 lo0
172.16.0.57 172.16.0.58 UH 3 0 utun1
$ route -n get 169.254.169.253
route to: 169.254.169.253
destination: 169.254.169.253
gateway: 192.168.1.254
interface: en1
flags: <UP,GATEWAY,HOST,DONE,b016,WASCLONED>
recvpipe sendpipe ssthresh rtt,msec rttvar hopcount mtu expire
0 0 0 0 0 0 1500 0
If I run this command it fixes things:
$ route -n modify 169.254.169.253 172.16.0.57 255.255.255.255
Interestingly if I watch the route table while tunnelblick is connecting I can see it go from the default gateway then to 192.168.1.254 then to 172.16.0.57 and finally back to 192.168.1.254 where it stays.
Haven't found a proper fix yet.