I cannot speak for other people, but personally I find nothing wrong with either インストールしています or インストール中. In both cases, the unstated subject is the installer or the computer.
On the other hand, インストールされています, mentioned in a comment, sounds definitely unnatural and “translationese” to me if it is used when a program is being installed. I guess that the reason is that されている usually means a state instead of an ongoing action in the passive form. For example, compare the following two sentences:
- Office をインストールしています。
- Office がインストールされています。
The former means that Office is currently being installed, while the latter will almost surely mean that Office exists on the system (as a result of installation in the past) just like the English sentence “Office is installed.”
In general, a computer or a program can naturally be a subject of actions in Japanese. For example, a hypothetical email client can show メールを送信しました after sending email messages. In English, this will probably be stated in the passive form such as “Messages (have been) sent.” If you feel that the passive form is more natural, that preference probably comes from the use of the passive form in your native language. In Japanese, メールが送信されました is ok, but the use of the passive form makes it sound slightly complicated for no good reason. メールを送信しました is just fine.