The compound is aromatic, it can be regarded as a modified styrene which in turn is a benzene derivative.
The compound contains a cyclic pi system which has 4n+2 pi electrons and is planar. Thus it is aromatic. It is normal not to count the pi electrons in side groups when counting the pi electrons in possible aromatic compounds.
For example benzoic acid has a carboxylic acid which has 2 pi electrons in it, these are not added to the total of the pi electrons in the benzene ring despite the fact that the benzene ring and the carboxylic acid can become coplanar thus allowing the pi systems of the two to overlap and join into a larger system.
If we consider naphthalene then this is a compound which has ring of ten carbons, half way around the ring there is a sigma bond which links one side of the ring to the other. Thus it can appear that naphthalene has two rings.
When we consider aromatic systems we should ignore sigma bonds, the sigma bonds may help to hold the molecule together but the sigma bonds which are within the nodal plane between the two sides of the pi system are unable to take part in the pi system.
We should be careful of the lone pair which I lightheartedly describe as "the bond to nowhere". In some aromatic compounds such as indole and thiophene one of the lone pairs on the heteroatom starts off in an atomic orbital which is a p orbital which then takes part in the pi system of the aromatic ring.
In other heterocycles such as pyridine the lone pair is in the nodal plane where the angular function of the wavefunctions of all the atomic orbitals which make up the pi system is zero. Thus there is no orbital overlap between the lone pair of a pyridine nitrogen and the pi system of the pyridine.
Be careful as in some cases such as pyrazole and oxazole there are both heteroatoms which contribute lone pairs to the pi system and other heteroatoms which only contribute a single electron (rather than a lone pair) to the pi system.