what does "having their attention increasingly fought for in repeat attempts" mean here?

Question

When it comes to marketing, nothing beats good old-fashioned get-in-you-hands, print. At least, nothing beats print when two things are happening. The first is that your audience is having their attention increasingly fought for in repeat attempts across multiple platforms. The second is that an older demographic still responds favorably to print; a younger demographic responds well to visually stimulating content, especially in print.

I know the meaning of all the word in this sentence but a whole sentence is ambiguous for me.

Answer 1

First of all, let's recall that have can be used (with a past participle) to express someone experiencing something.

have
2 b. used for saying that something happens to you or you experience something
​　　have something done (=something happens to you): While they were on vacation, they had their car broken into.

Now let's have a look at your sentence:

The first is that your audience is having their attention increasingly fought for in repeat attempts across multiple platforms.

The passage mentions a condition when two things are happening, and this sentence is about the first one. Breaking the sentence down like this should make it more obvious:

The first is that
​　　　your audience
​　　　　　is having their attention
​　　　　　　　increasingly fought for
​　　　　　　　　　in repeat attempts across multiple platforms.

So your audience is having their attention fought for (by the media, I presume) in such repeat attempts. In other words, many people (or the media) are fighting for the attention of your audience.