I can not speak to the specific computer you're look at however generally speaking there should be no problem installing VMware Player/Workstation on a Host System that has no Ethernet however using a Bridged Virtual Network Adapter with WiFi can/may be problematic. This can be so for a variety of reasons some of which are due to how Switches/Routers can/may be configured and others can/may be issues with the Host and or VMware Virtual Network. Over the years I've seen many different scenarios where using using a Bridged Virtual Network Adapter with WiFi can be problematic and sometimes the workaround is easy and acceptable and other times not.
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