You do not have to enter the W2-G for your dependent on your tax return.  Because he is under the filing threshold amount, the income will not be included on a tax return.  The filing requirement for a dependent is:

The standard deduction for an individual who can be claimed as a dependent on another person's tax return is generally limited to the greater of:

1. $1,100, or

2. The individual's earned income for the year plus $350 (but not more than the regular standard deduction amount, generally $12,200).

You do NOT enter a depended income on your tax return.   It can only go on the dependents own tax return if the dependent is require to file. 

I do not understand why you think the dependent does not have to file since gambling is unearned income (unless he is a professional gambler) and the filing requirement is over $1,100 of unearned income.

2020 Filing requirements for dependents.

Single dependents— (Not age 65 or older or blind)

You must file a return if any of the following apply.
1. Your unearned income was more than $1,100.
2. Your earned income was more than $12,400.
3. Your gross income was more than the larger of—
a. $1,100, or
b. Your earned income (up to $12,050) plus $350.

Or Dependent had net earnings from self-employment of at least $400. 

However, if any tax was withheld, then Dependent might want to file anyway to get a refund of the tax withheld.

Also, a person that CAN be a dependent cannot claim him/her self and must check the box that says that another taxpayer can claim them (whether or not that taxpayer actually claims him/her).

Note: your state filing requirements might be different than the federal.