Why didn't "spiel" get spelled with an "sh"?

Spiel derives from German spielen not from American Yiddish like the other terms you mention (boldface mine):

• "glib speech, pitch," 1896, probably from verb (1894) meaning "to speak in a glib manner," earlier "to play circus music" (1870, in a German-American context), from German spielen "to play," from Old High German spilon (cognate with Old English spilian "to play"). The noun also perhaps from German Spiel "play, game."

Source: Etymonline

Wiktionary hints at a possible relation with the Yiddish term shpil from which probably the alternative pronunciation originates:

• From the German Spiel ‎(“game, performance”), perhaps via Yiddish שפּיל ‎(shpil). Cognate with Old English spilian ‎(“to revel, play”).

JOSH's answer resolves the central question posed by MrHen. With regard to similar words adopted from German into English without inclusion of an h in the anglicized spelling, perhaps the closest match to spiel is spritz. Here is the entry for that word in Merriam-Webster's Eleventh Collegiate Dictionary (2003):

spritz 'sprits, 'shprits vb {G fr. spritzen} (1902) : spray ~ vi : to disperse or apply a spray

According to Leo Rosten, The Joys of Yinglish (1989) there is a Yiddish-English form of spritz, and he spells it with an h (shpritz):

shpritz (verb and noun) shpritzer (noun) Yinglish. From German/Yiddish: spritzen: "to sprinkle," "to spray," "to squirt."

Rosten doesn't list a Yiddish/English equivalent form of spiel. However, The American Heritage Dictionary of the English Language, fifth edition (2011) cites the Yiddish shpil (derived from Middle High German spil) as a possible direct source of spiel in English:

spiel (spēl, shpēl) Informal n. A lengthy or extravagant speech or argument usually intended to persuade. intr. & tr.v. spieled, spieling, spiels To talk or say something at length or extravagantly. {German, play, or Yiddish, shpil, both [from] Middle High German spil [from] Old High German.}

The Eleventh Collegiate dates spiel in English to 1870 and gives only one pronunciation for it: 'spēl . This surprises me because I have heard 'shpēl frequently enough to think of it as a common alternative pronunciation. Likewise the Eleventh Collegiate says that the second syllable of the curling term bonspiel is pronounced 'spēl (not 'shpēl )—although it certainly was pronounced with a sh sound in Calgary, Alberta, in the early 1970s, when I lived there. In any case, Merriam-Webster thinks that bonspiel, may be derived from Dutch bond (league) + spel (game); this word's first known occurrence in English is ca. 1770, so it has been in the language much longer than the standalone German-derived spiel.

Any discussion of English spiel should disregard Yiddish, which is irrelevant to its etymology. The word comes solely from German.

For details, see pages 563-570 of David L. Gold's Studies in Etymology and Etiology (With Emphasis on Germanic, Jewish, Romance, and Slavic Languages).