Does "Latin America" Refer Only to Middle America (Mainland + Islands)?

No. "Latin America" is a linguistic-cultural concept, not a purely geographic one limited to Middle America.

Definition

Latin America comprises all countries/territories in the Americas where Romance languages (Spanish, Portuguese, French) are predominant — legacy of Spanish, Portuguese, and French colonization.

Scope

• Mexico (North America)
• Central America (7 countries)
• South America (10 countries + French Guiana)
• Caribbean (Cuba, Dominican Republic, Puerto Rico, Haiti, Guadeloupe, Martinique, etc.)

Excluded

• English-speaking: USA, Canada (except Québec), Belize, Guyana, Jamaica, Bahamas, etc.
• Dutch-speaking: Suriname, Aruba, Curaçao, etc.

Thus, Latin America = ~20 sovereign states + several territories — spanning two continents and the Caribbean, far beyond "Middle America" (Mexico + Central America).