In principle, the Penguin Subtitle Player seems to support HTML formatted text, e.g. subtiles with <i> and </i> tags are rendered italic:

1
01:42:13,365 --> 01:42:21,723
- <i>This includes all the marine vessels.</i>

However, I have found that if there are two lines of text and only the second line contains HTML tags, then the tags are ignored and show up literally:

2
01:42:56,429 --> 01:43:02,198
- The war is over, my love. The war is gone.
- <i>This includes all the marine vessels.</i>

If the first line of text also contains HTML tags, then the formatting works, but the line break itself gets ignored:

3
01:43:09,731 --> 01:43:17,464
- The <i>war</i> is over, my love. The war is gone.
- <i>This includes all the marine vessels.</i>

The cause of these issues appears to be the line break. If a <br> tag is used instead of a real line break, then it works fine:

4
01:43:23,731 --> 01:43:30,464
- The war is over, my love. The war is gone.<br>- <i>This includes all the marine vessels.</i>

In fact, even if the <br> tag is then followed by a real line break, it still works:

5
01:43:38,139 --> 01:43:45,479
- The war is over, my love. The war is gone.<br>
- <i>This includes all the marine vessels.</i>

By the way, I took these screenshots on Windows 10 version 2004. I haven't tested this on other operating systems.

My suggestion to fix these issues would be as follows:
While parsing the .srt file, whenever you encounter a line break (inside a subtitle text block) that isn't already preceded by a <br> tag, simply insert a <br> tag right before it.
What do you think? Would that be possible?