It's not a matter of it being a computer word, as he already said. It's just that "email" is treated both as a mass and a count noun. So saying both:

"Check your email" and
"He just sent me 4 emails"

is acceptable. This occurs with some other words as well, though usually it has to do with containers. Like "I love beer" and "I had 4 beers last night". Email is just treated as a countable noun, so unless you want to start saying "e-letter", then you'll have to accept that "email" can be pluralized. There is no "correct" way to say it other than what is popularly understood or accepted.