Day trading is supposed to be trading within the day.
People making less than one trade per day are not day traders. Day traders should be profiting from smaller fluctuations, rather than the big leaps in price that can happen in cryptocurrencies over just a few days.
In other stocks and commodities, you could use day trading as part of an overall strategy, but in cryptocurrencies they're too wild to do both at the same time.
There are a few cryptocurrencies which have been stable enough to make day trading feasible, such as MAID and LSK. However, I wouldn't recommend day trading any cryptocurrency, because they are not particularly liquid and can violently break out of their trend at any time, leaving the profits you get from the tiny fluctuations seeming insignificant.
You're right on the first point, but not the second. Day traders are speculators but not necessarily gamblers which you'd have to be if you make trades you must close within the day even if there aren't any signals or patterns for you to analyse. Day traders enter and exit markets on the same trading day to manage risk, but won't enter at all if they can't see a point for entering.
Also, scalpers who take advantage of big leaps in price are also technically day traders. Their trades are executed in seconds. Gdax will remember how thousands of trades were executed during the flash crash. Also, who says you can't do day trading (or at least potential scalping) as part of overall strategy for crypto?