MATL, 4 bytes
Yf&= - For almost-primes the output is a matrix containing only ones
1s, which is truthy. - Otherwise the output is a matrix containing several ones
1s and at least a zeroone0, which is falsy.
Try it online! Or verify all test cases, including truthiness/falsihood test.
How it works
% Implicit input Yf % Prime factors. Gives a vector with the possibly repeated prime factors &= % Matrix of all pair-wise equality comparisons % Implicit output