Hello! Well apparently Valve ships the .so for HL2:DM in their GCF, so you can with next to no effort get it running on Linux (I had some odd crashes though)
If something about this seems unclear, I’ve explained some of the steps better in another guide

Half-Life 2: Deathmatch

1. Get the GCF “half-life 2 deathmatch.gcf”
2. Extract with GCFScape from nemesis.thewavelength.net
3. Move the hl2mp folder to ~/.Steam/SteamApps/<username>/Counter-Strike Source/
4. echo 320 > ~/.Steam/SteamApps/<username>/Counter-Strike Source/steam_appid.txt
5. ~/.Steam/SteamApps/<username>/Counter-Strike Source/hl2.sh -steam -game hl2mp

Day of Defeat: Source

1. Get the GCF “day of defeat source.gcf”
2. Extract with GCFScape from nemesis.thewavelength.net
3. Move the dod folder to ~/.Steam/SteamApps/<username>/Counter-Strike Source/
4. echo 300 > ~/.Steam/SteamApps/<username>/Counter-Strike Source/steam_appid.txt
5. ~/.Steam/SteamApps/<username>/Counter-Strike Source/hl2.sh -steam -game dod

Thanks to Flaming Sapz for confirming Day of Defeat: Source for me.
He also mentioned that Linux users should extract .gcfs with VIDE.

Title	Date
Steam What a mess you have made!	24 February 2013
Half-Life 2 Deathmatch on Linux	20 February 2013
Steam in a Clean Environment	12 February 2013
SteamLUG Game Night 2	10 February 2013
Steam Tools for Linux	06 February 2013
SteamLUG Game Night	02 February 2013
Half-Life mods on Steam for Linux	27 January 2013
Double Fine Adventures	20 January 2013
Steam for Linux and something else	16 January 2013
Dir Colors Script	20 October 2012