The term definitely predates D&D - the term "twenty dollar gold piece" has been in use for the $20 Double Eagle and $10 Eagle coins of the late 19th century, and also the $5 gold coin, as well.

"Gold Piece" In Print

The term is used in the Lebanon Daily News, 1 Nov 1965, of Lebanon, Pennsylvania, bottom, in an advert for old coins under the left column of text (to the right of the comics)

Four gold pieces: One (1) $20.00 gold piece, two (2) $10.00 gold pieces and one (1) $2.50 gold piece.

This alone establishes the phrase "gold piece" for gold coins in routine use prior to D&D. But let us press a little further back... say, 1913? Here's a quote from the 5 August 1913 Cedar Rapids Evening Gazette, from Cedar Rapids, Iowa, page 4, top of the third column:

The five cent piece ls the day laborer of our coinage. It la the hardest working and most successful bit at money In use In these United States. The twenty dollar gold piece Is very popular and is madly sought after In the best society; the five dollar bill has millions of friends and the hard silver dollar can be found nestling In the pocket of almost every man. But none of these like the five cent piece.

We thus have established a pattern of use for gold coins of being called "gold pieces" in the press, spanning over 5 decades; clearly not a D&D origin; not even viably a wargaming origin, for 1913 is the year of the first printing of H. G. Wells' Little Wars, the first commercially released set of wargaming rules in book form.

Searching Project Gutenberg, several ebooks have it in use...

These without clear denomination prefixed:

• Pinocchio (1883, Tr. ??? )
  Author: Carlo Collodi, 1826-1890
  Translator: Carol Della Chiesa, 1887-
• The Younger Set (1907)
  Author: Robert W. Chambers
• A Drama on the Seashore
  Author: Honore de Balzac (1799-1850)
  Translator: Katharine Prescott Wormeley (1830-1908)
• Tiger Cat (1938)
  Author: David H. Keller
• Pâkia (1901)
  Author: Louis Becke

And several with clear denomination in dollars:

• The Corner House Girls in a Play – How they rehearsed, how they acted, and what the play brought in
  Authors: Grace Brooks Hill, R. Emmett Owen
• The Young Bank Messenger (1898)
  Author: Horatio Alger, Jr
  

Piece

Piece is, according to several dictionaries, a common term for coins in general, of whatever denomination is specified. The quote below is excerpted from the etymology online page:

piece
early 13c., "fixed amount, measure, portion," from O.Fr. piece (11c.), from V.L. *pettia, probably from Gaulish (cf. Welsh peth "thing," Breton pez "piece"), from O.Celt. base *pett-.
[...]
Piece of Eight is the old name for the Spanish dollar (c.1600) of the value of 8 reals.

Commentary

It's pretty clear that it's a generic term for a gold coin, and for several US gold coins as well. In the US, it seems to be predominantly the popular $5 coin of the late 19th and early 20th centuries, but can be used collectively for the $2.50, $5.00, $10.00 and $20.00 gold coins; The silver coins of similar values were $0.10, $0.25, $0.50, and $1.00. Note that, still to date, "2 bits" is $0.25... a reference to the not uncommon practice of breaking Pieces of Eight (Dollares, or Reals) into 8 "bits" of an eighth-dollare each... I suspect that this is the origin of the 20:1 Silver:Gold ratio in AD&D...

It came from the fans of White Wolf's World of Darkness games. "Splat" is another name for the asterisk character ('*'), which is often used as a placeholder or "wild card" in a name by technical types of people. Someone somewhere starting referring to all of WW's various Clanbook/Tribebook/Guildbook/Kithbook supplements for their various games as "*books", pronounced "splatbooks."

From there, the term expanded out into the fans of other publishers' game lines that also followed a publishing scheme that offered player-facing supplements based on in-setting organizations or classes of characters. TSR had already been publishing The Complete X's Handbook supplements, and it naturally was applied to them in quick order. Between the vast market share held by the combination of White Wolf and TSR in the 90s, the term was virtually guaranteed to become commonplace—and it did.

Shannon Appelcline looks at the origin of the term "splatbook" in Designers & Dragons: The 90s in the chapter on White Wolf:

Splatbooks had been around since almost the dawn of roleplaying. […] However, no one had previous put out splatbooks as consistently and in such volume as White Wolf did. Clanbook: Brujah (1992) was the first. […] White Wolf would go on to produce splatbooks for all of their initial lines, and the term "splatbook" was eventually coined for White Wolf's releases.

…and again in the appendix entry, "10 Things You Might Not Know About Roleplaying in the ’90s: 1. The Splatbook Cometh":

The biggest change for the industry in the ’80s may have been the appearance of the splatbook. […] However, no one followed in GDW's footsteps until the very end of the ’80s. Only then did TSR kick off a new era of RPG publications with their PHBR series of Complete Handbooks for various AD&D classes (1988–1995). White Wolf followed and typically gets more credit for the splatbook revolution because they published a lot more. Starting with Clanbook: Brujah (1992) for Vampire: The Masquerade, each World of Darkness got its own series[…] In fact, White Wolf's extensive sets of splatbooks generated the term, with *book (pronounced "splatbook") referring to a book with a title noun at the start like “Clan” or “Tribe”.