From: http://www.thefreedictionary.com/flit:

flit (flt)
intr.v. flit·ted, flit·ting, flits
1. To move about rapidly and nimbly.
2. To move quickly from one condition or location to another.
n.
1. A fluttering or darting movement.
2. Informal An empty-headed, silly, often erratic person.

Noun 1. flit - a sudden quick movement
dart
movement, motility, motion, move - a change of position that does not entail a change of location; "the reflex motion of his eyebrows revealed his surprise"; "movement is a sign of life"; "an impatient move of his hand"; "gastrointestinal motility"
2. flit - a secret move (to avoid paying debts); "they did a moonlight flit"
move, relocation - the act of changing your residence or place of business; "they say that three moves equal one fire"
Great Britain, UK, United Kingdom, United Kingdom of Great Britain and Northern Ireland, Britain, GB - a monarchy in northwestern Europe occupying most of the British Isles; divided into England and Scotland and Wales and Northern Ireland
Verb 1. flit - move along rapidly and lightly; skim or dart
dart, fleet, flutter
butterfly - flutter like a butterfly
hurry, travel rapidly, zip, speed - move very fast; "The runner zipped past us at breakneck speed"


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Note added at 26 mins (2006-10-23 20:24:27 GMT)
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Would any of those definitions or synonyms fit the action of the scene?

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Note added at 1 hr (2006-10-23 21:03:55 GMT)
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This seems to suggest that 'flighting' is sometimes used as the gerund form of 'fly (as in 'flee' ('flighting' rather than 'flying') :

http://tinyurl.com/ydf8sv

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Note added at 1 hr (2006-10-23 21:10:41 GMT)
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There's also this:

http://tinyurl.com/yekzlm ????



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Note added at 1 hr (2006-10-23 21:12:20 GMT)
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And this:

http://tinyurl.com/yk3qyd

gioielli's and Caryl's answers must be the closest in terms of pronounciation; but, to me, it's a bit off when applied in the context.

It is said that "Ian is losing on time". In chess, it means Ian did not make a required number of moves during his assigned time. (AFAIK, you must make 40 moves in 2 hours in world championship, but pls consult chess sites for sure).

So, fleeting and flitting (= moving or passing rapidly) could be OK when applied to time, but looks weird when applied to Ian. In fact, he must be slow in making moves, so he lost on time.

I offer flirting in this sense: deliberately expose oneself to (danger or difficulty). So, in previous moves, Ian might make a speculative move that was ill-calculated. He might flirt w/ a sacrifice or a blitzkrieg that turned out to be a blunder (see chess glossary for the meaning). Consequently, he was time-pressed in his next moves and eventually beaten by the clock.

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Note added at 12 hrs (2006-10-24 08:07:57 GMT)
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... he was time-pressed = he had to take long time to make next moves as to compensate for the blunder he made.

Just a guess really. The other alternatives seem mighty odd.

I also agree with Erich, especially if one opponent is romantically interested in the other: Ian's losing the game is a means by which he flirts with his opponent.

Otherwise 'fighting' might work: the implication being 'This is how Ian fights - by losing the game'. More context might help.