With some exceptions (discussed below), Japanese kanji is mostly intelligible to people who can read Traditional and Simplified Chinese. One helpful contributing factor is the compositionality of many Chinese/Sino-Japanese expressions, which you could intuit the meaning of by identifying what the individual characters mean. A person who is unaware of a specific Japanese usage might still be able to guess the meaning this way. At the text level, context also helps.
The banner text in all three orthographies as follows:
Japanese: 自由民主党青年局 女性局主催 総裁選挙 公開討論会
Traditional Chinese: 自由民主黨青年局 女性局主催 總裁選舉 公開討論會
Simplified Chinese: 自由民主党青年局 女性局主催 总裁选举 公开讨论会
Simplified Chinese reduces some characters further than Japanese, but there's still broad agreement.
In the banner text, the only phrase that might be unfamiliar to Chinese readers is 主催, which is somewhat archaic. However, context and compositionality should allow a reader to infer the meaning.
So a Chinese reader would understand the text, word by word, as the following, resorting to compositionality if the phrase is unfamiliar:
[free/liberty] [democracy] [political party] [youth] [bureau] [female] [bureau]
[main/to be in charge + to urge] [chairperson/president/CEO] [election] [open to public] [discussion] [meeting/association].
From there, most would guess that it says something like 'Liberal Democratic Party Youth Bureau / Women's Bureau sponsoring Chairperson Election Open Forum'.
The modern equivalent of 主催 is 主辦/主办. 女性局 is more likely to be phrased as something like 婦女局/妇女局. Aside from those two differences, it's fairly idiomatic Chinese.
The exceptions listed in the beginning usually involve phrases that have gone through significant semantic drift in either language, some wasei-kango, and ateji. These include some very common words, so being unfamiliar with them could lead to serious misunderstanding. Examples include 勉強 ('study' in Japanese, 'reluctant/to do with difficulty/to force someone to do something' in Chinese), 私 ('I' in Japanese, 'self/private' in Chinese), 大丈夫 ('alright' in Japanese, 'real man' in Chinese), and so on.
However, these are also unlikely to occur in kanji-only environment outside of 伪中国语. Thanks to pop culture, some Chinese readers with no knowledge of Japanese may still be aware of the more common false friends. 大丈夫 and 大変 (大變/大变), for instance, are occasionally used with the Japanese meanings in Internet slang.