If you didn’t know the teams, you might think this was about one team, the Hanshin Giants.
Dropping 対 (“vs.”) is very common especially in the context of professional baseball games organized by 日本野球機構 (NPB), a counterpart of Major League Baseball of the US. You can optionally insert 中黒 (・) between 阪神 (Hanshin Tigers) and 巨人 (Yomiuri Giants).
Baseball fans call each NPB team in a different abbreviation way.
- 阪神タイガース (Hanshin Tigers owned by Hanshin Railway) → 阪神 (Hanshin)
- 読売ジャイアンツ (Yomiuri Giants owned by Yomiuri Newspaper) → 巨人 (Kyojin, as a translation from “Giant”)
- 東京ヤクルトスワローズ (Tokyo Yakult Swallows owned by a beverage company Yakult) → ヤクルト (Yakult)
The Tigers and the Swallows are called by the names of the owners. But few people call the Giants as 読売. I don’t know why.
阪神 and 巨人 are popular teams and their match is often called “阪神巨人伝統の一戦”.
Another similar expression you may want to memorize is
- セパ交流戦; meaning "Interleague games between the Central League and the Pacific League of NPB