They may have reported this as income from Detroit and withheld Detroit city tax, but gambling winnings by non-residents are not subject to Detroit City tax.
(If they withheld Detroit city tax, you could voluntarily file a return to get a refund).
The casino doesn't know what your residency status is, so they will report all winnings as "Detroit income". As a non-resident, however, you are not subject to Detroit city tax on that type of income.
For non-residents, Detroit City tax only applies to salaries, wages, bonuses, commissions, or other compensation for services rendered for work done or services performed in Detroit; net rental income from real and tangible personal property located in Detroit; net profit from a business, profession or other activity as a result of work done, services rendered or activity conducted in Detroit; capital gains less capital losses from the sale of real or tangible personal property located in Detroit.
