Run a PowerShell script on a different server - from inside a SQL Server job
If you are within a domain environment you can setup a proxy account that has permissions on SQLBILON1. However, using remote PowerShell is a bit of overkill and adds an unneeded layer to troubleshoot. If you do not have remote PowerShell enabled on both servers and firewall access between the servers configured properly it will have issues.

I would simply use UNC paths to the server. Whether you use the admin share like \\SQLBILON1\H$\SQLBackups or create share directly to \\SQLBILON1\SQLBackups. Unless you want to give the SQL Agent service on MYSQLSERVER1 permissions to that backup directory you would need to create a proxy account that has the appropriate permissions.

Your script will be much more simply if you just go this route:

#-------------------------------------------------------------------------------
# Script to delete old SSAS backup files
#
# Marcelo Miorelli
# 
# 19-novembre-2014 Wed
#-------------------------------------------------------------------------------


#-- set the Path where the backup files (.abf) are located
#
$path = '\\SQLBILON1\H$\SQLBackups' # OR \\SQLBILON1\SQLBackups

#-- set the number of days backups should be deleted -- in this case 2
#
$NumberOfDays = 2

#-- calculate the date of the backup files - if they are older than $days they will be deleted
#
$days = (Get-Date).AddDays(-$NumberOfDays)

#--get the list of the backup files to be deleted and delete them
#
Get-ChildItem $Path -Recurse '*.abf' | ? {$_.CreationTime -lt $days} | Remove-Item