Is there an easy way to compare which airfare search engines cover which airlines?

I see two questions here:

1. Is there an easy way to compare which airfare search engines cover which airlines?

I'm not aware of any. Some sites publish a list of the airlines they cover, e.g. Kayak has a ranking here and Azair has a list of them on their landing page, but others don't seem to publish this information. I remember having seen something like 400+ airlines for expedia and 900+ for Google Flights but I can't even find those numbers again.

2. Is there an easy way to see if other, competing airfare search engines would display prices for those airlines?

You have to check those competing airfare search engines. Note that Southwest does not allow aggregators to show their flights in their results but I would be surprised if that were the case for Emirates. Some seach engines, notably ITA Matrix, do not display flights of low-cost carriers. This summary answer of mine might be of tangential use to you. Here I found an older (and likely out-of-date) post about airlines that are typically not in flight search engines.

Your best strategy is to compare two or three search engines and take the best offer. There are quite complex algorithms behind flight searches and results can diverge or miss the optimum if you rely on only one engine.

In my experience the very best flight search engine is the ITA Matrix. I believe it is so comprehensive that it negates the need for a 3rd party website to list which websites return which airlines. Note that you cannot book flights on this site.

I am yet to find a scenario where this search engine wouldn't return a flight option (aside from airlines that specifically chose to exclude their fares such as Southwest Airlines).