Is the crime of rape an exception to the "two witnesses" rule?
Quick answer: no. Death penalty crimes always requires two or more witnesses for conviction.
25 But if the man finds the lady who is pledged to be married in the field, and the man forces her and lies with her, then only the man who lay with her shall die; 26 but to the lady you shall do nothing. There is in the lady no sin worthy of death; for as when a man rises against his neighbor and kills him, even so is this matter; 27 for he found her in the field, the pledged to be married lady cried, and there was no one to save her. Deuteronomy 22:25-27WEB
This passage must be read in the light of what Moses had preached just minutes before:
15 One witness shall not rise up against a man for any iniquity, or for any sin that he sins. At the mouth of two witnesses, or at the mouth of three witnesses, shall a matter be established. Deuteronomy 19:15WEB
The crime of rape is not (as some have alleged) "the only crime which can be established upon the testimony of only one witness." Moses was not contradicting what he had just preached, nor was he establishing an exception to the general rule stated in Deut. 19:15.
In fact, many Biblical case laws do not talk explicitly about witnesses, but any case law which mentions a civil penalty implies that there were witnesses. This fact is how we can know that the mere absence of a "signs of virginity" cloth does not, by itself, prove the guilt of the girl in Deut 22:15-21. See Is the premarital unchastity case of Deut. 22:13 an example of the justice system assuming guilt until a defendant proves her innocence?.
There must always be at least two witnesses in Biblical law, and the witnesses must throw the first stones: Deut. 17:6-7. Jesus affirmed this in John 8:7.
So what facts must be implicit in the case to allow the death penalty?
The girl cried out, and no one was there to hear her and prevent the rape. However, a witness (family member?) encountered the rape in progress. Probably the girl was either threatened with harm if she cried out further, or somehow muffled by the terrain or an action by her assailant.
No one was there to save her from being raped, but at least one person (plus the girl herself) could act as probative witnesses.
The purpose of the phrase "the betrothed young woman cried out" in v. 27 is to establish that the woman was not consenting to the encounter -- in other words, to distinguish this from the previous case of adultery (Deut. 22:22-24). This case therefore establishes the legal principle that a rape victim's claim in court that she cried out "in the country" -- even if no one heard it -- must be accepted as legally sufficient to exculpate her from guilt of adultery.
Her testimony must be considered sufficient to clear her from guilt, but it is not legally sufficient in and of itself to convict the person whom she is accusing.
- see also Deut. 17:6