A few moments after it happened you opened the scoreboard, and you have the setting where net_graph 4 is enabled with the scoreboard. This graph has enough history which covers the event.
http://i.imgur.com/bdhprDm.png
Note the spikes in the middle, each multicolored vertical line represents a packet of data (the colors are for different types of data). Note specifically how they are much taller during the lag (more updates in each packet), and that there are less of them (some appear to be missing).
This does look like packet loss to me.
Interestingly this loss corresponded with your player model contacting an enemy model (the soldier jumping by). The TF2 client visually moves your character when you use the movement keys before getting a server confirmation of those movements, this makes moving around feel immediate and not laggy (the alternative is you having to wait your ping time to move, ew!). This works pretty well when you're interacting with just the map, since the client and server use the same logic to map movement keys to physical translation, and the server agrees with what the client predicted.
This gets much harder when you run into an enemy model. The issue is that your client still predicts your movement (it has to for the game to feel right), but the information your game has on the enemy's position is out of date (because pings) so the actual interaction between your models can only be accurately resolved by the server. If you're running alongside an enemy your client may make predictions that are getting constantly corrected, creating an effect where the models appear to telelport around.
So overall:
-It looks like there was some packet loss
-Your player model touched an enemy player model in an unpredictable way at the same time
TF2 Smooths most of these transitions, but in cases were the gap is too large it corrects everything in one go.