Justin,
Yes the issue is the esriRequest. The code format you are using is for 4.x and will not work in 3.x.
in 3.x it looks like this:
var layersRequest = esriRequest({
url: "https://earthquake.usgs.gov/ws/designmaps/asce7-16.json",
content: { "latitude": 18, "longitude": -66, "riskCategory": "I", "siteClass": "D", title="Default"},
handleAs: "json",
callbackParamName: "callback"
});
layersRequest.then(
function(response) {
var seis_data = response.response.data;
console.log("Success: ", response.response.data);
}, function(error) {
console.log("Error: ", error.message);
});