Apart from Bitcoin, Elon hasn't explicitly asked anyone to invest in any other cryptocurrency. If you look at his tweets related to DOGE coin, it can be seen that he has never asked his twitter followers to invest in it. Neither has he claimed that DOGE is a good speculative investment asset. But as you said, Elon is like a double edged sword. If he can pump the prices with his tweets, for sure he can cause a drop as well.
Yes, he played around his tweets very smartly. He created polls and asked followers whether dogecoin to the moon or other cryptos to the moon which ultimately created an image among investors and traders that he is putting dogecoin against all other cryptos which sounded like something big is going to happen with the dogecoin.
It's similar to asking chips vs the fast food poll, then although not promoting you are consciously pushing the value of chips
![Grin](https://bitcointalk.org/Smileys/default/grin.gif)
People went crazy because it was a kind of domino effect, when one buys a coin, others follow and hence the price keeps rising because everyone is buying looking at each other until the trend stops and the dump starts. I have no doubt that EM musked the price for dogecoin for whatever intention he had.