That API key is for integration into your own iOS apps, eg something coded and submitted via the app store, not for use from within FileMaker Go itself.
GoMaps might be a good starting point for your project, it already has a lot of google maps integration worked out for you:
If you want to use that API, you might have to set up your own web service (generating a browser API key), that you can call into FileMaker via Insert From URL or into a webviewer.
I already have the logic, I am doing a lot with the maps, working great.
Plotting geobox for prospects, referal locations etc.
However what happened is after i went live with it out on the road the Google API is throwing errors something like "This device or IP is not allowed to use this API" so unless I'm in the company umbrella IP wise (as setup in the allowed IP's in the Key) I can't use the API and the mapping fails.
I'll look into that web service avenue see what I can come up with.
How does everyone deal with the API calls from mobile devices in Go?
Google allows up to 25,000 map loads and up to 2500 address lookups per day, but I can't seem to get it to work without actually using a Key. I will play with it some more and see what I can come up with.