In my desktop workflow I have steps that will assign to a different user. In the desktop version they are able to execute to the next step. However, this same step cannot be executed in the Web edition. It is unnecessary for me to create groups for these steps.
There are a few things you can check to ensure the correct steps are being used and they are configured correctly.
These workflow steps are not JTX Desktop specific steps. They are normal Procedural & Question steps that do not do any other operation. I looked in the workflows and the supported platform is set to "both" by default for every step.
The workflow on the Web Edition allows the user to complete/execute the steps if the job is assigned to them. However, once a step is assign to a new user the new user is unable to complete/execute the assign steps. The complete step ribbon on the Web Edition disappears.
I think what is happening is that you have step assignment set on your workflows in the administrator. On the desktop there are tools to assign a step to the current user. It is a 2 step process, first the job is assigned to the user and then you have to explicitly assign the step to the user as well.
I recommendation we started to make is for our users to use the path assignment now, since this will assign the job to the group and there is no need for you to take that additional step to assign the step to a user/group.
This is a link to a blog that was written about that - Workflow Manager: Path vs. Step Assignment
With regards to the execution tools, we are going to improve that user experience so that the execution tools are only disabled and do not disappear when a user cannot execute the workflow.
I hope this helps.
I was also able to replicate a similar process using the JTX reassign jobs to force the job to be reassign to a group. I did this because I noticed a user was able to work through the workflow if they were assigned to the same group.