Yes they do, but they are allowed more income before they have to file and it is dependent on the status of the senior.
A single senior has to make over $10,750 before they have to file a tax return. If the senior is filing jointly as a couple and only one of them is a senior their gross income has to be over $19,800 before they have to file. If both members of the couple are seniors then their gross income must be above $20,900.
As a head of household the gross income for the senior must be over $12,000. A widow with a dependent child gross income must be over $16,150. If a senior that is married but filing separately has only a limit of $3,650 before they must file a tax return.