First of all, day trading is no more gambling than any other trading. If the price rises you ride the wave, if it doesn't you wait until it does. That's pretty much all. In this sense, if day trading is gambling, then all trading is essentially gambling. Besides, arbitrage is also day trading which involves quite a few trades (actually, twice as many) albeit it is anything but gambling.
You are incredibly wrong here and very misguided. Day trading absolutely is gambling. It is gambling because it is luck based and not based on any type of valid research or methodology. Strategies for trading assets intra-day by looking at charts do not lead to consistently outperforming the market over the long term, and there are tons of studies and data out there that show this. Almost no day traders consistently beat the market in which they are trading as a whole.
Profit earned is all that counts in the end. Note that I'm not saying that day trading is profitable for everyone or it is a losing game for every trader out there. But it simply can't be gambling if you accept that trading as such is not gambling. There is no other choice because all price growth starts small, even profits from long-term investment are made of small price moves. Capitalizing on the volatility which results from these small moves allows you to earn higher profits because there is no growth without corrections, however small those can be. Add to this that you can't always be right in your assessment of the future growth and even more so in respect to the extent of it.
And you completely write off arbitrage which belongs to day trading as much as day trading is concerned.
What statistic are you talking about that suggests the best trading strategy would be capitalizing on both short term volatility and long term growth? It sounds like you are just saying the best way to trade is sell at the top of every peak and buy at the bottom of every dip. This is not realistic.
You would need to use trading bots for that and take into account trading fees obviously. Ultimately, it all comes down to how efficiently you allocate your trading capital so as not to lose profit on bigger price moves. It looks like you think that day trading excludes any possibility of "seeing a long-term value in an asset". This is another misconception, of course.