The fee is subsumed (under taxes) in the estimated total price at booking, so it's not an extra charge. Hotwire and Priceline guests will be none the wiser as they prepay in full and can't get itemized folios.
Of course, the fee is disrespectful to customers and unfair to other hotels because the HGI room rate will be misleadingly low on hotel comparison search engines.
I will celebrate the day when hotels, like airlines, must advertise total prices.