The Israelites had been defeated in war by an enemy army much smaller than theirs; so the ironic question points out that this incredible defeat—one enemy soldier routing a thousand Israelites—could happen only because the LORD was no longer fighting for them.
The verse is in the form of a rhetorical question, which may be effective in some languages; in many, however, if not in most, a rhetorical question may be misunderstood and should thus be translated as a strong statement.
How should one chase a thousand: that is, “How could one [enemy] soldier put to rout [or chase, or put to flight] one thousand [Israelite] soldiers?” or, as a statement, “The only reason why one enemy soldier defeated one thousand Israelite soldiers was….” Good News Translation offers another good model.
Two put ten thousand to flight: or “two enemies defeated ten thousand.” This is parallel, but it heightens the sheer absurdity of the matter.
Their Rock had sold them: see verse 4; sold means that Yahweh sold (or, abandoned) them to the enemy (see Judges 2.14; 3.8; 4.2; 10.7).
The LORD had given them up: that is, he had abandoned them (see 23.15).
An alternative translation model for this verse is:
• One enemy soldier defeated a thousand Israelite soldiers,
and ten thousand Israelites were defeated by two of their enemies.
This is because Yahweh, their mighty protector [or, Rock],
has abandoned them to their enemies,
and has let their enemies defeat them.
However, in some languages it may be better to reverse the order of the lines as follows:
• The Mighty God sent his people away,
the LORD abandoned them.
That is why one enemy [soldier] routed a thousand [Israelites],
two enemy soldiers put ten thousand Israelites to flight.
Quoted with permission from Bratcher, Robert G. and Hatton, Howard A. A Handbook on Deuteronomy. (UBS Helps for Translators). New York: UBS, 2000. For this and other handbooks for translators see here .

Thank you! This verse now makes perfect sense to me.