No.  He is showing you how Mailmerge fields are nested in IF fields to
perform AND/OR logic.

The IF field doesn't support AND and OR. (Have a look in Word Help for the
syntax of these fields!)

If you prefer to use AND and OR explicilty, you can use the following
approach

Use { COMPARE }  to make the comparisons, e.g.

{ COMPARE a = b }

gives 1 if a = b and 0 if a <> b

then use the and and or functions within the { = } field to do the logic:

{ =and(a,b) } is 0 if a is 0 or b is 0, and 1 if a and b are 1

then wrap that inside an IF to give the result you need

{ IF { =and(a,b) } = 1 "result if both a and b are non-zero" "result if
either a or b is 0" }

e.g. to take your example,

{ IF { =or({ COMPARE { MERGEFIELD Appt_Provider } = "Provider1"  },
{ COMPARE { MERGEFIELD  Appt_Provider } = "Provider 2" }) } = 1 "Yes",
"No" }

(I think!)

You can nest ors and ands within the { = } field but notice that in the case
of multiple ors you can should also be able to use

{ IF { ={ COMPARE { MERGEFIELD Appt_Provider } = "Provider1"  }+
{ COMPARE { MERGEFIELD  Appt_Provider } = "Provider 2" } } > 0 "Yes", "No" }

Not the way I'd design the "field language" but there you go.