Source is episode 2.
I usually like to keep my clips to 2 minutes in length or less. I had a really, really hard time finding a clip of around that length for this show. This is a show that takes its time with its storytelling and builds up a story over the course of an entire episode.
If you aren't familiar with this series at all, it is an adaptation of a novel series in which Kino travels across a world with their trusty motorrad (a sentient motorcycle), visiting different countries. It's an anthology series, so each episode is a self-contained story (or more than one). The anime adapts some of the most popular stories contained within the novel series.
This story, centered around the Colosseum, has been adapted twice. In the first anime series from 2003, it actually spans across two episodes, while in the 2017 version of the show it is condensed into a single episode. This quick montage of Kino advancing through the rounds of fights is part of how they save time in this story as this was more drawn out in the 2003 telling.
As for the show itself, it is an excellent series full of interesting stories, moral dilemmas, philosophical musings, and a splash of action to top it off. I highly recommend this series to people that like to think about their media. There are often scenarios in which Kino has to make a choice whether or not to intervene in a country's internal affairs because it contradict's their conscience or sense of justice. It has similar feelings to Star Trek's Prime Directive at times.
If you are a fan of shows like Mushishi or Natsume's Book of Friends, then Kino's Journey is going to scratch a similar itch. For modern viewers, I would probably recommend watching the 2017 version of the show. There are some different stories that each series adapts, so if you really like the 2017 version, then absolutely watch the 2003 version as well. In particular, one of my favorite episodes is only adapted in the 2003 version, but it can be difficult to watch for many modern viewers because of the artistic style it employed.
Anyway, watch this show. It is great.