That looks like the app won’t work because it looks like it relies on OpenSSL 1.0 or 1.1. Both of which are not available in Rocky 9. Now if you were using Rocky 8, you would be fine:
[root@rocky8 ~]# dnf provides */libssl.so.10
Last metadata expiration check: 4:15:30 ago on Tue 21 May 2024 06:49:59 AM CEST.
compat-openssl10-1:1.0.2o-4.el8_6.i686 : Compatibility version of the OpenSSL library
Repo : appstream
Matched from:
Filename : /usr/lib/libssl.so.10
compat-openssl10-1:1.0.2o-4.el8_6.x86_64 : Compatibility version of the OpenSSL library
Repo : appstream
Matched from:
Filename : /usr/lib64/libssl.so.10
As you can see compat-openssl package exists which provides that library. Use Rocky 8 instead or ask the vendor to update their application to support OpenSSL 3 which Rocky 9 has.