Exporting Illustrator files to PNG in sequence

Instead of Adobe Media Encoder, you'll want to use Image Processor in Photoshop.  It's found under File > Scripts > Image Processor....

To get to PNG, you'll have to create a Save action that chooses PNG as the file format.  If your Illustrator files are CMYK, you'll also need Convert Mode action before the Save action.

Step 3 of the Image Processor requires saving to a JPEG, PSD and/or TIFF.  If you want transparency in your resulting PNGs, choose PSD.  (If you happen to also want JPEGs, you could enable that as well.)

When the process is complete, you'll have whatever file format you chose in step 3 and the PNGs that you created in step 4.  You can delete the step 3 files if you don't want to keep them (but they are necessary in order to get to step 4 and can't be avoided).

It can take a little trial and error, but I've put this to use a few times in the past.

Image Processor is also available in Adobe Bridge.  I just haven't ever tried to convert AI to PNG using Bridge.

The action that you'll need to get to PNG.

Image Processor settings that have worked for me.

More information here:

Process a batch of Photoshop files

Adobe Media Encoder wasn't designed to convert AI files to PNGs. You can copy each of your illustrator files to a single document, each on their own artboard, then export each artboard to a PNG.