Someone doing short term trade beating the market over a long period? It doesn't seem to happen.
If trading includes writing/selling options, then yes, it does seem to happen; plenty of businesses make their money writing options. Whether the options are long-term or short-term, the writer takes a premium above the expected value of the option; otherwise what's their incentive to sell?
This isn't a violation of the EMH or a suggestion that the past predicts the future. (The trending strategy, OTOH, is). Writing options actually adds new (financial) products into the market, rather than trying to make money buying and selling stocks that already exist. If you create new products to sell, I don't see a finance-theoretic reason you can't beat the average person buying and selling stocks that already exist.
That said, economic theory still applies; you aren't the only one writing options, so your premiums have to be low enough to be competitive. Chances are, you'd be making more flipping burgers, because the algorithmic trading software you're competing with has more capital and more time, and doesn't ask for minimum wage.