Why is the boiling point of a parent alcohol higher than that of a product alkene?

boiling point depends on the intramolecular forces attracting the molecules to each other.  The stronger the forces the higher the boiling point.  An alcohol has hydrogen bonding contributing the the intermolecular forces.  H-bonding is much higher than the London dispersion force (temporary dipoles) which is the main intermolecular force in the alkene product of your elimination reaction.  The higher the forces attracting the molecules the more energy required to get the vapor pressure to atmospheric pressure and thus the higher the boiling point.