Preparation

This Guide assumes you are using the latest (as of this writing, ESXi 6.7) host client on a free install of ESXi, not the VSphere client. Options may be slightly different for that client.

Download Alpine and upload to a reachable Datastore

For this guide, I used the latest Virtual Images, which at the time was, 3.10.2

Create VM Options

Name: Choose any name you like
Compatibility: Linux
Guest OS Version: Select Other 5.x or later Linux (64-bit) if you downloaded the x86_64 Alpine-ISO, or Other 5.x or later Linux (32-bit) if you downloaded the x86 Alpine-ISO.

Edit VM Settings once Created

The default alpine linux iso images only boot from bios, not the ESXi default of UEFI for Linux 4.0+ hosts. To get around this limitation, you have three options:

Change the VM to use Bios Boot
1. Make sure the VM is powered off. (If it is on, you will not be able to change boot options, and your save will fail.)
2. Right click on the VM, and select Edit Settings
3. Select VM Options
4. Under Boot Options > Firmware, select bios
5. Click save.
You could create a new ISO image following the Create UEFI secureboot USB guide (outside the scope of this guide)
You can change the VM Compatability options to Other Linux (64-bit) but you loose the VMXNET and SR-IOV Passthrough NIC options (helpful for a virtualized firewall) and are limited to the E1000 NIC driver which has been known to drop network connectivity.

Installation

Install Alpine Linux. I used the default setup-alpine script

Post-Install

Install and enable Open-VM-Tools

Enable the Community repo

using root/sudo/wheel privileges, edit /etc/apk/repos and un-comment the community repo

Install open-vm-tools

apk add --update open-vm-tools

Start, and enable at boot. As of this writing the open-rc scripts are included in the base open-vm-tools package instead of a separate -openrc package.

rc-service open-vm-tools start rc-update add open-vm-tools