Uh, no. Humans aren't "apes". Not by standard convention. The argument is that humans should be classified as apes if both chimps and gorillas are, because chimps are more closely related to humans than they are to gorillas.
The premise here is that a taxon should always include ALL descendant species on a given limb (and ALL its branches) beyond a given branching node. This is the contention especially of "cladistic" taxonomy.
IOW if gorillas branch off first, THEN chimps and humans split, you have to call all three species by the same group name, and whatever you call gorillas you must also call both humans and chimps. You can only distinguish humans and chimps from gorillas by putting them together in some subgroup.
However this type of cladistic taxonomy is NOT the conventional form, and is probably neither practical or workable if implemented exclusively, completely and consistently. We're always going to have to sometimes and somehow recognize that particular lineages are sometimes sufficiently "divergent" with respect to others within their "clade" that they warrant a different name.
For example, by the exact same logic that humans are "apes," humans (and chimps and gorillas) are also "reptiles". It turns out that cladistically there are no such things as "mammals". I.e. there's no way to separate mammals from ALL reptiles (or rather the reverse) by a single branching event. The reason is that mammals branched off from reptiles very early, then there are lots of other reptiles (that we insist on calling reptiles) and then birds branch off from reptiles.
You can't (by the cladistic logic) then call reptiles, mammals and birds by different names that all have the same "rank". And yet we do. Further you can't call mammals anything different from (all of what we call) reptiles, since mammals (and birds) are simply a lineage within reptiles.