Not Dummy Coding, but similar? HELP!

#1
I've been asked to code ethnicity in a way that is similar to dummy coding but it's not dummy coding. I'll give an example of how I recoded the variable into dummy variables, how I've been asked to make the dummy variables look, and then ask some questions about this dummy-like coding. The person requesting this variable also does not know what this coding type is called and is convinced that it is dummy coding, so I'm trying to figure it out and have come out with nothing after many searches (online, in textbooks, etc.).

Example: We have 6 ethnic groups coded as follows
White = 1
Latino = 2
Asian = 3
African American = 4
Other = 5
Mixed = 6

This is the transform --> recode syntax I used to create the dummy variables with Latinos as the reference group:

RECODE
ethnicity2
(1=1) (2=0) (3=0) (4=0) (5=0) (6=0) INTO dummyWhite .
VARIABLE LABELS dummywhite 'if 1, then case white'.
EXECUTE .


RECODE
ethnicity2
(1=0) (2=0) (3=1) (4=0) (5=0) (6=0) INTO dummyAsian .
VARIABLE LABELS dummywhite 'if 1, then case asian'.
EXECUTE .

RECODE
ethnicity2
(1=0) (2=0) (3=0) (4=1) (5=0) (6=0) INTO dummyAfAmer .
VARIABLE LABELS dummywhite 'if 1, then case african american'.
EXECUTE .

RECODE
ethnicity2
(1=0) (2=0) (3=0) (4=0) (5=1) (6=0) INTO dummyOther .
VARIABLE LABELS dummywhite 'if 1, then case other'.
EXECUTE .

RECODE
ethnicity2
(1=0) (2=0) (3=0) (4=0) (5=0) (6=1) INTO dummyMixed .
VARIABLE LABELS dummywhite 'if 1, then case mixed'.
EXECUTE .

The person requesting this wants the variables to look this way:
If we are dummy coding for white cases, white cases should have the value of 1, Latino cases should have the value of 0, and Asian, African American, Other, and Mixed should have no value at all.

What is this coding called and why would you use it over dummy coding? Can this coding be used in analyses the same way as dummy coded variables?

Any help is appreciated.