It seems to be slang relatedto the game Netrunner; all Google searches seem to lead there. It's impressive how obscure the language is, I thought I'd understand things easily by context but I can't even figure out how the game works. The best clue I found to its meaning is here:
http://boardgames.stackexchange.com/questions/15589/what-are-some-common-tactics-to-make-runs-against-servers-with-unrezzed-ice-in-nhttps://boardgames.stackexchange.com/questions/15589/what-are-some-common-tactics-to-make-runs-against-servers-with-unrezzed-ice-in-n
The most relevant section:
Run with a click (and two credits) to spare, especially against NBN (and some Weyland). Tags are a genuine threat, and Corps won't ever try to tag you without having something nasty round the corner. Scorched Earth is a game-defining card. Your last click should be reserved for clearing a tag until you know you won't need to.
Soo, it looks like "running" is a game action, and "clicks" are resources required to do actions, and "running on your last click" appears to be ill-advised because you might need that last click for some other purpose after you run ?
The video you link to doesn't say much (otherwise you wouldn't be posting here presumably), other than paraphrasing this principle as "Instead of spending energy trying to be smart, try not to be stupid".
Putting all this together I might suppose the speaker is saying, don't make super-elaborate, utterly optimized plans (I figure people are tempted to "run on their last click" because they use all of the clicks before on very smart strategic preparation ?) that risk falling apart once something unexpected happens (like getting "tagged" by a Corp ?).
That's all I've got, you can probably get better info on a Netrunner forum, on Stack Exchange or Reddit.
