I can confirm this on archlinux. With glibc version 2.25-7 the service still worked. Upgrade glibc to version 2.26-3 and the service fails to start with that exact error:
[ztefn@arch-linux]: ~>$ sudo /opt/logmein-hamachi/bin/hamachid debug 09.11 18:16:22.013 cfg: load() 09.11 18:16:22.015 dbg: deploy_id '' parse failed 09.11 18:16:22.015 cfg: hkc set: [2048] [2048] 09.11 18:16:22.015 cfg: save() 09.11 18:16:22.028 cfg: hks: [0] [2048] 09.11 18:16:22.029 cfg: hkc: [0] [2048] [2048] 09.11 18:16:22.029 starting up .. 09.11 18:16:22.029 sys: version linux-2.1.0.174 09.11 18:16:22.031 sys: os Linux 4.12.12-1-ARCH #1 SMP PREEMPT Sun Sep 10 09:41:14 CEST 2017 x86_64 09.11 18:16:22.032 vpn: IPv6 support is: 3 09.11 18:16:22.032 ipc: 5 listening at /var/run/logmein-hamachi/ipc.sock 09.11 18:16:22.033 avc: start 09.11 18:16:22.033 09.11 18:16:22.033 avc: retry 2, [1] sys: initializing vpn domains, vpn-reinstall = 0 .. 09.11 18:16:22.035 vpn: added [Hamachi] domain (not roaming) 09.11 18:16:22.036 dbg: setup_vpn_domain [Hamachi] 09.11 18:16:22.036 dbg: vpn_domain::config - [Hamachi] 09.11 18:16:22.037 vpn: switched [Hamachi] domain into L3 mode, 25.113.141.116/255.0.0.0 09.11 18:16:22.037 dbg: enable(Hamachi), locked: 0 09.11 18:16:22.037 vpn: domain [Hamachi] -> 'VPN_opening' 09.11 18:16:22.037 vpn: enabling [Hamachi] domain .. 09.11 18:16:22.037 vpn: on_set_tapdev(, 1) -> ok 09.11 18:16:22.037 tap: device ham0 opened 09.11 18:16:22.039 vpn: domain [Hamachi] -> 'VPN_up' 09.11 18:16:22.039 dbg: setup_vpn_domain [Hamachi] 09.11 18:16:22.039 dbg: vpn_domain::config - [Hamachi] 09.11 18:16:22.039 vpn: domain [Hamachi] -> 'VPN_setting_up' 09.11 18:16:22.039 tap: config(ham0, 25.113.141.116, 255.0.0.0, [/96]) 09.11 18:16:22.043 tap: if_config() -> 1 09.11 18:16:22.043 vpn: tap config done, [ok] 09.11 18:16:22.043 vpn: domain [Hamachi] -> 'VPN_up' 09.11 18:16:22.043 vpn: added [Null] domain (not roaming) 09.11 18:16:22.043 dbg: setup_vpn_domain [Null] 09.11 18:16:22.043 dbg: vpn_domain::config - [Null] 09.11 18:16:22.068 vpn: arp, 25.113.141.116 is at 7a:79:19:71:8d:74 09.11 18:16:22.083 avc: retry 2, [2] 09.11 18:16:22.135 avc: retry 2, [3] 09.11 18:16:22.185 avc: retry 2, [4] 09.11 18:16:22.235 avc: retry 2, [5] 09.11 18:16:22.287 avc: th_end 09.11 18:16:22.287 avc: warning, avc not ready, fallback 09.11 18:16:22.287 resolv: url has ip on it 09.11 18:16:22.566 ses: on_ip_change() 09.11 18:16:23.826 vpn: gratitious arp for local ip 09.11 18:16:25.287 avc: retry 1, [1] 09.11 18:16:25.288 resolv: url has ip on it 09.11 18:16:28.287 avc: retry 1, [2] 09.11 18:16:28.288 resolv: url has ip on it 09.11 18:16:31.287 avc: retry 1, [3] 09.11 18:16:31.287 resolv: url has ip on it 09.11 18:16:34.287 avc: retry 1, [4] 09.11 18:16:34.287 resolv: url has ip on it 09.11 18:16:37.287 avc: retry 1, [5] 09.11 18:16:37.287 resolv: url has ip on it 09.11 18:16:40.287 avc: false, f: [send], e: [71] 09.11 18:16:40.287 avc: on_avc_res, [1], [0] 09.11 18:16:40.287 avc: send later at sync 09.11 18:16:42.209 ipc: user ztefn allowed 09.11 18:16:42.209 ipc: 01441960 add client 1 09.11 18:16:42.210 cfg: save() 09.11 18:16:42.223 cfg: hks: [0] [2048] 09.11 18:16:42.223 cfg: hkc: [0] [2048] [2048] 09.11 18:16:42.223 sys: connmgr_go_online, reconnect 0 09.11 18:16:42.267 ses: on_conn_state(connected, 0x0) 09.11 18:16:42.267 ses: select conn mode 'dns lb' 09.11 18:16:42.268 ses: go_offline, keep_tunnels 1, login_on_relaunch 0, actual state 4 .. 09.11 18:16:42.306 sys: go_online, reconnect 0 09.11 18:16:42.325 ses: resolving hamachi-dc.logmein-gateway.com .. 09.11 18:16:42.359 ses: resolving hamachi-list.10.logmein-gateway.com ..hamachid: relocation error: hamachid: symbol __res_maybe_init, version GLIBC_PRIVATE not defined in file libc.so.6 with link time reference