It doesn't necessarily look old. That's just your opinion. I see some answers that haven't read the guidelines you linked so I'm going to highlight this first.
The ellipses is used to indicate that this button requires a follow-up interaction.
Simply replacing it with something else wouldn't work in all occasions.
While there may be other ways to accomplish this, you have to think of where this came from, and about why you'd be replacing it.
Would you be replacing it because you feel it's old? Is old a problem? Did it stop working? A table is a pretty old thing, and they are still used. Spoons. Forks. Sure the spork attained cult status, but it hasn't replaced the other tools. Because they work!
So where did the ellipsis come from? Literature. Consider these two lines.
One of these has a future! The ellipsis illustrates there's more to that statement than just those words. Something else is coming.
Ellipsis have been around for ages (Wikipedia gives us 1588 as the first occurance) and will probably be around for many more. This means that people will inherently understand it, in most languages even.
There might be ways to replace it, but none will be as consistently recognisable.