this seems to be very similar to ZBX-9867

Steps to reproduce:
go through steps listed on
https://www.zabbix.com/download?zabbix=3.4&os_distribution=ubuntu&os_version=xenial&db=MySQL

Result:
? zabbix-server.service - Zabbix Server
Loaded: loaded (/lib/systemd/system/zabbix-server.service; enabled; vendor preset: enabled)
Active: active (running) since Thu 2018-04-12 15:14:33 PDT; 3s ago
Process: 1982 ExecStop=/bin/kill -SIGTERM $MAINPID (code=exited, status=0/SUCCESS)
Process: 1985 ExecStart=/usr/sbin/zabbix_server -c $CONFFILE (code=exited, status=0/SUCCESS)
Main PID: 1989 (zabbix_server)
Tasks: 1
Memory: 2.2M
CPU: 33ms
CGroup: /system.slice/zabbix-server.service
??1989 /usr/sbin/zabbix_server -c /etc/zabbix/zabbix_server.conf

Apr 12 15:14:33 zbx systemd[1]: Starting Zabbix Server...
Apr 12 15:14:33 zbx systemd[1]: zabbix-server.service: Failed to read PID from file /run/zabbix/zabbix_server.pid: Invalid argument
Apr 12 15:14:33 zbx systemd[1]: zabbix-server.service: Supervising process 1989 which is not our child. We'll most likely not notice when it exits.