Most HTML 5 games actually are clones of older games or have clones of themselves in flash or whatever. For example, Bejewled has dozens of similar games from Pokemon Trozei (easy) to
Seven Wonders (hard but fun). There's a good chance the "exclusive" game can be found elsewhere with different art and a different name where it can be played offline. As the vast majority of HTML 5 games are ripoffs of other games that can be found elsewhere, it's really not worth the time and effort to try to locate all the assets and save every last bit of them. You could probably buy any of them from any App store for under $5, buy a better version from Good Old Games, or find a ROM or Vaporware and play it for free.
Even if you did take the hours of time and painstaking effort to save one tiny HTML5 game, HTML5 is not the only language that runs them as HTML5 is pretty much all graphics and layout stuff with no backend to make it "go". If the game's backend is actually written in server-side language like MYSQL, it won't run without a server even if you did get every single file. That's because server-side languages are made to be accessed from a website only! You could try to set things up so it reads like a server without being online, but that is a major headache and easy to get wrong. ROMS, Vaporware, or just buying games are your best bet.
If you'tr trying to make a massive arcade by downloading someone's entire games website, know this: There's a good chance that your brother will only really play 1 in 10 games. Too much choice will make him skip through the games, get bored with most of them fast, and only really play his small handful of favorites. There's a strong chance that he might even not have any favorites and call all the games "kids junk" as most HTML5 games really are for the very casual and very young crowd. To avoid this, you need to find out what games he likes. Tell him you are looking for "games like this" and won't get him the exact same games, then focus on his likes.
Also, downloading a random games site in it's entirety is a bad idea as games can have varied quality, especially when they're free "HTML5" games. You'll need to play each game as far as you can go to be sure there's no game breaking bugs, microtransactions, pay walls (buy to continue) or other bad junk in there As you're going to have to do this anyway regardless of what games you pick, why not focus on high quality games instead? Sometimes having only a couple good games is best. Remember growing up when getting a new game was a real treat? Now, share the joy by adding games slowly, carefully, and picking the best ones.
What games were you wanting in specific? Half of the softgames games won't load on my machine but I can look at them and guess some similar games.