If you are playing over DLNA, everything is different. After all, you aren't actually on the PC that is running the MC Server, so the MC Server which has the Subtitle file isn't even rendering the video. Naturally, the MC OSD doesn't exist on the Renderer (even if it is another instance of MC, but why would you do that over DLNA?) using the right-click method isn't going to activate a MC menu.
So try this first. On your MC Server open "Options > Media Network > Add or configure DLNA servers... > Advanced > Present Subtitle Resources", and tick that box. Now with the correct settings for Subtitles in "Options > Video > Subtitles & Language" MC should try to display the Subtitles, and if your DLNA Renderer is capable of turning on and presenting Subtitles, try turning them on and see if that works. You will have to work out how to do that on your DLNA Renderer.
If the above doesn't work, and if you can play the video on the MC Server, then do so and select the Subtitle stream that you want and make any adjustments so that they display properly with the video, and then go back to your DLNA Renderer and see if the Subtitles now work. Note that you can check if Subtitles are set to play on a video by looking at the [Playback Info] tag, which will include something like this text;
(1:5)(12:SubtitleSize)(1:1)(16:SubtitleTimingMS)(4:2500)(7:Streams)(3:0,1)(9:Subtitles)(25:SRT [Oblivion (2013).srt])(14:SubtitleShiftY)(1:0)
As you can see, there are a few Subtitle parameters in that text. The bold bit turns on the Subtitles and selects the Subtitle SRT file in this case.
If you can't play the video on your MC Server because it is headless or something like that, then you can also just edit the [Playback Info] tag directly and add in the parameters that you require. See the image below for some more examples of what the [Playback Info] tag may look like. The two highlighted Movies are good examples. You may have to experiement a bit if you are editing the tag directly, because some of the parameter components are inconsistent. i.e. The number before the ":SRT" in the examples changes.