There are essentially two parts to the message:
- Grammarly helps a lot of people write more clearly and effectively every day
- Grammarly operates across multiple platforms and devices
Some will say the last things said will be retained more readily. This is true in longer messages (paragraphs, essays, chapters, books, etc). It is probably a very minimal factor in the two simple messages above.
Some will say that the first thing read in a longer sentence is the thing people will key on for meaning and then kind of blow through the remainder. In that case, the most important thing would be first.
If there is any difference, it is a very weak distinction.
Grammerly probably considers their notional goal is improving writing but technically it is important that they also make people aware of their service functioning on multiple platforms and device types. Both are important to their success so it is arguable that there is no distinction (but equally, I think you could argue that either of the two premises they are communicating could be more important).
You could have written:
Grammarly’s digital writing assistant, operating across multiple platforms and devices, helps over 20 million people write more clearly and effectively every day.
As I often see people read the first few words of a sentence then tune out, I'd say the first thing you want to convey should be presented at the start. But others might say the most important part is the last thing read, assuming the reader reads the entire sentence.
I think from a grammar point of view, there is nothing to suggest and difference of meaning between either versions of the original poster's examples.