I just built an AR, and I had to pay a FFL fee to the person I shipped my lower receiver to.

Now I'm planning on buying a shotgun from Gander Mountain.  

My question is: Do I have to pay their incredibly expensive FFL fee to get the shotgun?  Or does that not apply to shotguns?

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You pay whatever fee they charge.  If you don't like their prices, don't buy there or have it shipped there.  There are plenty of FFL's that do transfers for $25 and under, why would you go to Gander ?

I talking about buying a gun in-store.  I'm curious if they charge a FFL fee for shotguns because I actually have no idea if that's even a thing.

I'm planning on going there because their 870 Remington Express's are like $300.  So if I have to pay $75 for a FFL fee, I'll go somewhere else.

Not complaining, just asking to save the most money.

The FFL fee you paid was probably a "transfer" fee which is standard practice for incoming transfers, and prices range from $20 on up.  If you rbuying a gun from an FFL(Gander or any of the type) you typically don't pay the transfer fee, as the FFL seller already has added in there profit markup.  I charge $20 for transfers of firearms, and $50 for suppressors.  As for firearm purchases, i have a flat rate "markup" that i apply to the firearm for my time, and am totally up front and transparent on all my costs to my customers.

If you buy a firearm (shotgun or otherwise) that an FFL has in-stock, you will not pay the transfer fee. The transfer fee is for firearms that you buy online or from a non-local FFL and have shipped to your local FFL to transfer to you. In that case, without the transfer fee, the FFL would not make a penny for his time of receiving your package, logging it into his books, providing you with the paperwork and instructions to fill it out, running the NICS check (if necessary), and logging the firearm out of his books.

If you go to Gander Mountain for the 870 Express, you'll pay whatever is on the tag plus tax. They may try to talk you into trigger locks, slings, cleaning supplies, cases, and ammunition, but that's all up to you. I wouldn't buy more than the gun from them. They do tend to have pretty good prices on the 870 Express from time to time.

Trigger lock comes with the gun, buyer signs a paper stating that they received such lock.

Yes, a cheap one. However, they've tried to talk me into the separate Master Lock ones and the combo packs with multiple locks using the same key.