Before diving into non-Steam methods, it's crucial to highlight the to play. You can actually get Half-Life Deathmatch: Source for free directly on Steam if you own other compatible titles.
You will spend 4 hours troubleshooting for 15 minutes of shooting a revolver at a wall. It is not worth it.
"A Comprehensive Analysis of Half-Life: Deathmatch Source - A Free, Non-Steam Downloadable Game"