What you're referring to is a date picker content control. So far, these can only be created on PCs and don't work on Macs for versions 2011 & earlier. What you have access to via your screenshots is formfields. Formfields are supported on all Mac & PC Word platforms, but were not designed to be used in conjunction with content controls; doing to can lead to unexpected behaviour.

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Cheers,
Paul Edstein
[Fmr MS MVP - Word]

Thank you. So would it be possible to create a data field that calculates the number of days based on the start and end dates?

I basically want the figure out how to calculate a total based on the entries

number of days
number of pets
any special options or needs, etc

for example
If I had departure date: (12/21/2017) based on their entry
return date: (12/25/2017) based on their entry
total: 4 days (calculated based on their input in previous two fields)

Eventually I would add the other elements